Optical filter and imaging apparatus

ABSTRACT

An optical filter (1a) includes a light-absorbing layer (10). The light-absorbing layer absorbs light in at least a portion of the near-infrared region. When light with a wavelength of 300 nm to 1200 nm is incident on the optical filter (1a) at incident angles of 0°, 30°, and 40°, the optical filter (1a) satisfies given transmittance requirements. IEθ1/θ2CR, IEθ1/θ2CG, and IEθ1/θ2CB defined for two incident angles θ1° and θ2° (θ1&lt;θ2) selected from 0°, 30°, and 40° satisfy given requirements. Ranges satisfy given requirements, each range being a difference obtained by subtracting the smallest value of IEθ1/θ2CR, IEθ1/θ2CG, and IEθ1/θ2CB defined for the same two incident angles θ1° and θ2° from the largest value of IEθ1/θ2CR, IEθ1/θ2CG, and IEθ1/θ2CB defined for the same two incident angles θ1° and θ2°.

TECHNICAL FIELD

The present invention relates to an optical filter and imagingapparatus.

BACKGROUND ART

Imaging apparatuses including an optical filter such as a near-infraredcut filter are conventionally known. For example, Patent Literature 1describes a near-infrared cut filter including a laminated sheet havinga near-infrared-absorber-including resin layer provided on at least oneside of a glass sheet substrate. For example, this near-infrared cutfilter has a dielectric multilayer film provided on at least one side ofthe laminated sheet. For this near-infrared cut filter, the absolutevalue |Ya−Yb| of the difference between a wavelength value (Ya) and awavelength value (Yb) is less than 15 nm. The wavelength value (Ya) is avalue of a wavelength which lies in the wavelength range of 560 to 800nm and at which the transmittance measured in the directionperpendicular to the near-infrared cut filter is 50%. The wavelengthvalue (Yb) is a value of a wavelength which lies in the wavelength rangeof 560 to 800 nm and at which the transmittance measured at an incidentangle of 30° to the near-infrared cut filter is 50%. As just described,the angle dependence of the transmission characteristics of thenear-infrared cut filter according to Patent Literature 1 is adjusted tobe small.

Patent Literature 2 describes a near-infrared cut filter including anear-infrared-absorbing glass substrate, near-infrared-absorbing layer,and dielectric multilayer film. The near-infrared-absorbing layerincludes a near-infrared-absorbing dye and transparent resin. PatentLiterature 2 describes a solid-state imaging apparatus including thisnear-infrared cut filter and a solid-state imaging device. According toPatent Literature 2, the influence of the angle dependence whichdielectric multilayer films inherently have and which is anincident-angle-dependent shift of a shielding wavelength band can bealmost completely eliminated by laminating the near-infrared-absorbingglass substrate and near-infrared-absorbing layer. For example, inPatent Literature 2, a transmittance (T₀) at an incident angle of 0° anda transmittance (T₃₀) at an incident angle of 30° are measured for thenear-infrared cut filter.

Patent Literatures 3 and 4 each describe an infrared cut filterincluding a dielectric substrate, an infrared-reflecting layer, and aninfrared-absorbing layer. The infrared-reflecting layer is formed of adielectric multilayer film. The infrared-absorbing layer includes aninfrared-absorbing dye. Patent Literatures 3 and 4 each describe animaging apparatus including this infrared cut filter. Patent Literatures3 and 4 each describe transmittance spectra shown by the infrared cutfilter for light incident at incident angles of 0°, 25°, and 35°.

Patent Literature 5 describes a near-infrared cut filter including anabsorbing layer and a reflecting layer and satisfying givenrequirements. For example, the difference |T₀₍₆₀₀₋₇₂₅₎−T₃₀₍₆₀₀₋₇₂₅₎|between an integral T₀₍₆₀₀₋₇₂₅₎ of transmittances of light withwavelengths of 600 to 725 nm in a spectral transmittance curve shown bythis near-infrared cut filter at an incident angle of 0° and an integralT₃₀₍₆₀₀₋₇₂₅₎ of transmittances of light with wavelengths of 600 to 725nm in a spectral transmittance curve shown thereby at an incident angleof 30° is 3%·nm or less. Patent Literature 5 also describes an imagingapparatus including this near-infrared cut filter.

Patent Literatures 6 and 7 each describe an optical filter including alight-absorbing layer and near-infrared-reflecting layer and satisfyingΔE*≤1.5. ΔE* is a color difference between light having beenperpendicularly incident on the optical filter and transmittedtherethrough and light having been incident on the optical filter at anangle of 30° to the direction perpendicular to the optical filter andtransmitted therethrough. The light-absorbing layer includes, forexample, a binder resin, in which a light absorber is dispersed. Thenear-infrared-reflecting layer is, for example, a dielectric multilayerfilm. Patent Literatures 6 and 7 each also describe an imagingapparatus, such as a camera, including this optical filter.

CITATION LIST Patent Literature

-   -   Patent Literature 1: JP 2012-103340 A    -   Patent Literature 2: WO 2014/030628 A1    -   Patent Literature 3: US 2014/0300956 A1    -   Patent Literature 4: US 2014/0063597 A1    -   Patent Literature 5: JP 6119920 B2    -   Patent Literature 6: KR 10-1474902 B1    -   Patent Literature 7: KR 10-1527822 B1

SUMMARY OF INVENTION Technical Problem

The above patent literatures fail to specifically discuss thecharacteristics which would be exhibited by the optical filters whenlight is incident on the optical filters at an incident angle largerthan 35° (e.g., 40°). Moreover, in spite of the fact that imagingapparatuses such as cameras are equipped with an image sensor thatincludes a color filter having R (red), G (green), and B (blue), theabove patent literatures fail to discuss compatibility with thecharacteristics of such a color filter. Therefore, the present inventionprovides an optical filter that is likely to be compatible with thecharacteristics of a color filter used in an image sensor mounted in animaging apparatus even when the incident angle of light is larger andthat exhibits characteristics advantageous to prevent uneven coloring ofan image generated by an imaging apparatus such as a camera. The presentinvention also provides an imaging apparatus including this opticalfilter.

Solution to Problem

The present invention provides an optical filter including:

-   -   a light-absorbing layer that includes a light absorber absorbing        light in at least a portion of the near-infrared region, wherein    -   when light with a wavelength of 300 nm to 1200 nm is incident on        the optical filter at incident angles of 0°, 30°, and 40°, the        optical filter satisfies the following requirements:    -   (i) the spectral transmittance at a wavelength of 700 nm is 3%        or less;    -   (ii) the spectral transmittance at a wavelength of 715 nm is 1%        or less;    -   (iii) the spectral transmittance at a wavelength of 1100 nm is        7.5% or less;    -   (iv) the average transmittance in the wavelength range of 700 nm        to 800 nm is 1% or less;    -   (v) the average transmittance in the wavelength range of 500 nm        to 600 nm is 85% or more;    -   (vi) the spectral transmittance at a wavelength of 400 nm is 45%        or less; and    -   (vii) the spectral transmittance at a wavelength of 450 nm is        80% or more, and    -   in the case where the spectral transmittance of the optical        filter at a wavelength λ and an incident angle θ° is expressed        by T_(θ)(λ),    -   where functions of the wavelength λ are expressed by R(λ), G(λ),        and B(λ), the functions being defined by Table (I) in a domain        ranging between wavelengths of 400 nm and 700 nm,    -   where a normalization coefficient is calculated so that the        largest value of three functions being products of T₀(λ) and        R(λ), G(λ), and B(λ) is 1,    -   where functions defined by multiplying functions being products        of T_(θ)(λ) and R(λ), G(λ), and B(λ) by the normalization        coefficient are expressed by CR_(θ)(λ), CG_(θ)(λ), and        CB_(θ)(λ), respectively, and    -   where the wavelength λ being a variable of CR_(θ)(λ), CG_(θ)(λ),        and CB_(θ)(λ) is expressed by λ(n)=(Δλ×n+400) nm (Δλ=5) as a        function of an integer n of 0 or more,    -   IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB) defined        by the following equations (1) to (3) for two incident angles        θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° satisfy        requirements shown in Table (II), and    -   ranges satisfy requirements shown in Table (II), each range        being a difference obtained by subtracting the smallest value of        IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB) defined        for the same two incident angles θ1° and θ2° from the largest        value of IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2)        ^(CB) defined for the same two incident angles θ1° and θ2°.

TABLE (I) Wavelength λ (nm) R(λ) G(λ) B(λ) 400 0.100 0.066 0.429 4050.089 0.067 0.492 410 0.079 0.068 0.556 415 0.069 0.068 0.604 420 0.0590.068 0.653 425 0.052 0.072 0.691 430 0.045 0.076 0.728 435 0.040 0.0820.769 440 0.035 0.089 0.811 445 0.031 0.100 0.836 450 0.027 0.112 0.862455 0.026 0.133 0.868 460 0.025 0.153 0.875 465 0.026 0.213 0.863 4700.027 0.272 0.850 475 0.030 0.358 0.818 480 0.034 0.444 0.785 485 0.0360.523 0.732 490 0.038 0.602 0.680 495 0.042 0.669 0.615 500 0.046 0.7370.549 505 0.056 0.797 0.478 510 0.065 0.857 0.406 515 0.078 0.903 0.345520 0.091 0.948 0.284 525 0.096 0.974 0.245 530 0.101 1.000 0.206 5350.096 0.998 0.183 540 0.091 0.995 0.159 545 0.088 0.970 0.143 550 0.0850.944 0.126 555 0.090 0.907 0.110 560 0.096 0.870 0.093 565 0.141 0.8250.085 570 0.186 0.780 0.076 575 0.331 0.728 0.073 580 0.476 0.675 0.071585 0.651 0.616 0.070 590 0.826 0.556 0.070 595 0.897 0.485 0.066 6000.968 0.414 0.062 605 0.968 0.354 0.058 610 0.968 0.294 0.053 615 0.9570.255 0.054 620 0.947 0.216 0.055 625 0.932 0.200 0.055 630 0.918 0.1840.055 635 0.899 0.173 0.058 640 0.881 0.161 0.061 645 0.867 0.157 0.067650 0.853 0.152 0.073 655 0.837 0.155 0.078 660 0.822 0.157 0.084 6650.795 0.168 0.087 670 0.767 0.178 0.091 675 0.749 0.196 0.098 680 0.7320.215 0.105 685 0.718 0.237 0.108 690 0.705 0.259 0.111 695 0.704 0.2770.115 700 0.702 0.296 0.119

$\begin{matrix}{{IE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (1) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (2) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (3)\end{matrix}$

TABLE 2 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range −5 to 5 −5to 5 −5 to 5 0 to 4 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB)Range −5 to 5 −5 to 5 −5 to 5 0 to 4 IE_(30/40) ^(CR) IE_(30/40) ^(CG)IE_(30/40) ^(CB) Range −3 to 3 −3 to 3 −3 to 3   0 to 1.3

The present invention also provides an imaging apparatus including:

-   -   a lens system;    -   an imaging device that receives light having been transmitted        through the lens system;    -   a color filter that is disposed ahead of the imaging device and        is a filter of three colors, R (red), G (green), and B (blue);        and    -   the above optical filter that is disposed ahead of the color        filter.

Advantageous Effects of Invention

The above optical filter is likely to be compatible with thecharacteristics of a color filter used in an imaging apparatus such as acamera even when the incident angle of light is larger and exhibitscharacteristics advantageous to prevent uneven coloring of an imagegenerated by an imaging apparatus. Moreover, an image generated by theabove imaging apparatus of the present invention is unlikely to becolored unevenly even when the incident angle of light is larger.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a cross-sectional view of an example of an optical filter ofthe present invention.

FIG. 1B is a cross-sectional view of another example of the opticalfilter of the present invention.

FIG. 1C is a cross-sectional view of yet another example of the opticalfilter of the present invention.

FIG. 1D is a cross-sectional view of yet another example of the opticalfilter of the present invention.

FIG. 1E is a cross-sectional view of yet another example of the opticalfilter of the present invention.

FIG. 1F is a cross-sectional view of yet another example of the opticalfilter of the present invention.

FIG. 2 is a graph showing R(λ), G(λ), and B(λ).

FIG. 3 is a cross-sectional view of an example of an imaging apparatusof the present invention.

FIG. 4A shows a transmittance spectrum of an intermediate product of anoptical filter according to Example 1.

FIG. 4B shows a transmittance spectrum of another intermediate productof the optical filter according to Example 1.

FIG. 4C shows a transmittance spectrum of a laminate according toReference Example 1.

FIG. 4D shows transmittance spectra of a laminate according to ReferenceExample 2.

FIG. 4E shows transmittance spectra of the optical filter according toExample 1.

FIG. 5A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 1 at an incident angle of 0°.

FIG. 5B is a graph showing the normalized spectral sensitivity functionsof the optical filter according to Example 1 at an incident angle of30°.

FIG. 5C is a graph showing the normalized spectral sensitivity functionsof the optical filter according to Example 1 at an incident angle of40°.

FIG. 6A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 1 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 6B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 1 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 6C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 1 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 7A shows a transmittance spectrum of a laminate according toReference Example 3.

FIG. 7B shows transmittance spectra of an optical filter according toExample 2.

FIG. 8A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 2 at an incident angle of 0°.

FIG. 8B is a graph showing the normalized spectral sensitivity functionsof the optical filter according to Example 2 at an incident angle of30°.

FIG. 8C is a graph showing the normalized spectral sensitivity functionsof the optical filter according to Example 2 at an incident angle of40°.

FIG. 9A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 2 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 9B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 2 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 9C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 2 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 10A shows a transmittance spectrum of an intermediate product of anoptical filter according to Example 3.

FIG. 10B shows transmittance spectra of the optical filter according toExample 3.

FIG. 11A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 3 at an incident angle of 0°.

FIG. 11B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 3 at an incidentangle of 30°.

FIG. 11C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 3 at an incidentangle of 40°.

FIG. 12A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 3 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 12B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 3 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 12C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 3 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 13A shows transmittance spectra of a laminate according toReference Example 4.

FIG. 13B shows transmittance spectra of an optical filter according toExample 4.

FIG. 14A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 4 at an incident angle of 0°.

FIG. 14B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 4 at an incidentangle of 30°.

FIG. 14C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 4 at an incidentangle of 40°.

FIG. 15A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 4 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 15B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 4 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 15C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 4 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 16 shows transmittance spectra of an optical filter according toExample 5.

FIG. 17A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 5 at an incident angle of 0°.

FIG. 17B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 5 at an incidentangle of 30°.

FIG. 17C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 5 at an incidentangle of 40°.

FIG. 18A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 5 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 18B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 5 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 18C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 5 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 19A shows a transmittance spectrum of an intermediate product of anoptical filter according to Example 6.

FIG. 19B shows transmittance spectra of the optical filter according toExample 6.

FIG. 20A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Example 6 at an incident angle of 0°.

FIG. 20B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 6 at an incidentangle of 30°.

FIG. 20C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Example 6 at an incidentangle of 40°.

FIG. 21A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 6 at anincident angle of 0° and those at an incident angle of 30°.

FIG. 21B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 6 at anincident angle of 0° and those at an incident angle of 40°.

FIG. 21C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to Example 6 at anincident angle of 30° and those at an incident angle of 40°.

FIG. 22A shows transmittance spectra of an intermediate product of anoptical filter according to Comparative Example 1.

FIG. 22B shows a transmittance spectrum of a laminate according toReference Example 5.

FIG. 22C shows transmittance spectra of the optical filter according toComparative Example 1.

FIG. 23A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Comparative Example 1 at an incidentangle of 0°.

FIG. 23B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Comparative Example 1 at anincident angle of 30°.

FIG. 23C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Comparative Example 1 at anincident angle of 40°.

FIG. 24A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 1 at an incident angle of 0° and those at an incident angle of30°.

FIG. 24B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 1 at an incident angle of 0° and those at an incident angle of40°.

FIG. 24C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 1 at an incident angle of 30° and those at an incident angle of40°.

FIG. 25A shows a transmittance spectrum of an infrared-absorbing glasssubstrate of an optical filter according to Comparative Example 2.

FIG. 25B shows transmittance spectra of a laminate according toReference Example 6.

FIG. 25C shows a transmittance spectrum of a laminate according toReference Example 7.

FIG. 25D shows transmittance spectra of the optical filter according toComparative Example 2.

FIG. 26A is a graph showing normalized spectral sensitivity functions ofthe optical filter according to Comparative Example 2 at an incidentangle of 0°.

FIG. 26B is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Comparative Example 2 at anincident angle of 30°.

FIG. 26C is a graph showing the normalized spectral sensitivityfunctions of the optical filter according to Comparative Example 2 at anincident angle of 40°.

FIG. 27A is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 2 at an incident angle of 0° and those at an incident angle of30°.

FIG. 27B is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 2 at an incident angle of 0° and those at an incident angle of40°.

FIG. 27C is a graph showing differences between the normalized spectralsensitivity functions of the optical filter according to ComparativeExample 2 at an incident angle of 30° and those at an incident angle of40°.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described withreference to the drawings. The following description is directed to someexamples of the present invention, and the present invention is notlimited by these examples.

The present inventors have invented the optical filter according to thepresent invention based on new findings obtained from the followingstudies of optical filters.

An optical filter shielding against unnecessary light other than visiblelight is disposed in an imaging apparatus or a camera module mounted ina personal digital assistant such as a smartphone. The use of an opticalfilter including a light-absorbing layer has been discussed to shieldagainst unnecessary light. Like the optical filters described in PatentLiteratures 1 to 7, many optical filters including a light-absorbinglayer further include a reflecting film composed of a dielectricmultilayer film.

Interference of light reflecting on the front and back surfaces of eachlayer of a reflecting film composed of a dielectric multilayer filmdetermines a wavelength band of transmitted light and a wavelength bandof reflected light. Light can be incident on an optical filter atvarious incident angles. The optical path length in the reflecting filmincluded in an optical filter changes depending on the incident angle oflight incident on the optical filter. As a result, the wavelength bandsof transmitted light and reflected light shift to the short wavelengthside. Therefore, it is conceivable that in order not to greatly vary thetransmittance characteristics of the optical filter depending on theincident angle of light, the boundary between a wavelength band of lightto be blocked and a wavelength band of light to be transmitted isdetermined by a wavelength band of light absorption, and that awavelength band of light to be reflected by the dielectric multilayerfilm is separated apart from the wavelength band of light to betransmitted.

In Patent Literatures 1 and 2, the transmission characteristics of thenear-infrared cut filters for light incident at incident angles of 0°and 30° are evaluated. In Patent Literatures 3 and 4, transmittancespectra shown by the infrared cut filters for light incident at incidentangles of 0°, 25°, and 35° are evaluated. In recent years, cameramodules mounted in personal digital assistants such as smartphones havebeen expected to achieve a wider angle of view and a much lower profile.Therefore, it is desirable that the wavelength band and amount of lighttransmitted through optical filters be unlikely to vary even when theincident angle of light is larger (e.g., 40°).

When light is incident on an optical filter including a reflecting filmcomposed of a dielectric multilayer film at a large incident angle, thereflectance of light can locally increase in a wavelength band of lightreflection of which should be reduced to achieve a high transmittance.As a result, the optical filter involves a defect called a ripple, i.e.,a local decrease in transmittance. For example, even an optical filterdesigned not to produce a ripple upon incidence of light at an incidentangle of 0° to 30° tends to produce a ripple when the incident angle oflight is increased to 40°.

A measure has not yet been established for comprehensive evaluation ofthe effects arising from occurrence of a ripple and from anincident-angle-dependent shift of the boundary between a wavelength bandof transmitted light and a wavelength band of blocked light. Accordingto the technique described in Patent Literature 5, the boundary betweenthe wavelength band of visible light which is expected to be transmittedand the wavelength band of near-infrared light which is expected to bereflected or absorbed is stable with respect to a variation in incidentangle of light. However, the technique described in Patent Literature 5has room for improvement in view of occurrence of a ripple and anincident-angle-dependent shift of the boundary between the wavelengthband of visible light and the wavelength band of ultraviolet light.

In each of Patent Literatures 6 and 7, the characteristics of theoptical filter itself are determined with the use of a color differenceΔE*, but it does not ensure that the optical filter is compatible with apractical imaging apparatus. This is because R, G, and B segments of acolor filter each correspond to a pixel of an image sensor included inan imaging apparatus and the amount of light detected by each pixel ofthe sensor correlates with a product of a spectral transmittance of theoptical filter shielding against unnecessary light and a spectraltransmittance of each segment of the color filter. Therefore, opticalfilters desirably have characteristics compatible with thecharacteristics of a color filter used in an imaging apparatus.

Under these circumstances, the present inventors made intensive studiesto discover an optical filter that is likely to be compatible with thecharacteristics of a color filter used in an imaging apparatus even whenthe incident angle of light is larger. Additionally, the presentinventors made intensive studies to discover an optical filter thatexhibits characteristics advantageous to prevent uneven coloring of animage generated by an imaging apparatus. As a result, the presentinventors have invented the optical filter according to the presentinvention.

Herein, the term “spectral transmittance” refers to a transmittanceobtained when light with a given wavelength is incident on an objectsuch as a specimen and the term “average transmittance” refers to anaverage of spectral transmittances in a given wavelength range.Additionally, the term “transmittance spectrum” herein refers to one inwhich spectral transmittances at wavelengths in a given wavelength rangeare arranged in the wavelength order.

Herein, the term “IR cut-off wavelength” refers to a wavelength which isdetermined by incidence of light with a wavelength of 300 nm to 1200 nmon an optical filter at a given incident angle, which lies in thewavelength range of 600 nm or more, and at which the spectraltransmittance is 50%. The term “UV cut-off wavelength” refers to awavelength which is determined by incidence of light on an opticalfilter with a wavelength of 300 nm to 1200 nm at a given incident angle,which lies in the wavelength range of 450 nm or less, and at which thespectral transmittance is 50%.

As shown in FIG. 1A, the optical filter 1 a includes a light-absorbinglayer 10. The light-absorbing layer 10 includes a light absorber. Thelight absorber absorbs light in at least a portion of the near-infraredregion. When light with a wavelength of 300 nm to 1200 nm is incident onthe optical filter 1 a at incident angles of 0°, 30°, and 40°, theoptical filter 1 a satisfies the following requirements:

-   -   (i) the spectral transmittance at a wavelength of 700 nm is 3%        or less;    -   (ii) the spectral transmittance at a wavelength of 715 nm is 1%        or less;    -   (iii) the spectral transmittance at a wavelength of 1100 nm is        7.5% or less;    -   (iv) the average transmittance in the wavelength range of 700 nm        to 800 nm is 1% or less;    -   (v) the average transmittance in the wavelength range of 500 nm        to 600 nm is 85% or more;    -   (vi) the spectral transmittance at a wavelength of 400 nm is 45%        or less; and    -   (vii) the spectral transmittance at a wavelength of 450 nm is        80% or more.

Since the optical filter 1 a satisfies the above requirements (i) to(vii), the optical filter 1 a incorporated in a wide-angle-lens-equippedcamera module or imaging apparatus can shield against unnecessary lightwithout reducing brightness.

The spectral transmittance of the optical filter 1 a at a wavelength λand an incident angle θ° is expressed by T_(θ)(λ). Functions of thewavelength λ are expressed by R(λ), G(λ), and B(λ), the functions beingdefined by Table (I) below in a domain ranging between wavelengths of400 nm and 700 nm. A normalization coefficient is determined so that thelargest value of three functions being products of T₀(Δλ) and R(λ),G(λ), and B(λ) is 1. Functions defined by multiplying functions beingproducts of T_(θ)(λ) and R(λ), G(λ), and B(λ) by the normalizationcoefficient are expressed by CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ),respectively. CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) are also called hereinnormalized spectral sensitivity functions. The wavelength λ being avariable of CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) is expressed byλ(n)=(Δλ×n+400) nm (Δλ=5) as a function of an integer n of 0 or more. Onthe basis of these, IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2)^(CB) defined by the following equations (1) to (3) for two incidentangles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° satisfyrequirements shown in Table (II), and ranges satisfy requirements shownin Table (II), each range being a difference obtained by subtracting thesmallest value of IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2)^(CB) defined for the same two incident angles θ1° and θ2° from thelargest value of IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2)^(CB) defined for the same two incident angles θ1° and θ2°.

TABLE (I) Wavelength λ (nm) R(λ) G(λ) B(λ) 400 0.100 0.066 0.429 4050.089 0.067 0.492 410 0.079 0.068 0.556 415 0.069 0.068 0.604 420 0.0590.068 0.653 425 0.052 0.072 0.691 430 0.045 0.076 0.728 435 0.040 0.0820.769 440 0.035 0.089 0.811 445 0.031 0.100 0.836 450 0.027 0.112 0.862455 0.026 0.133 0.868 460 0.025 0.153 0.875 465 0.026 0.213 0.863 4700.027 0.272 0.850 475 0.030 0.358 0.818 480 0.034 0.444 0.785 485 0.0360.523 0.732 490 0.038 0.602 0.680 495 0.042 0.669 0.615 500 0.046 0.7370.549 505 0.056 0.797 0.478 510 0.065 0.857 0.406 515 0.078 0.903 0.345520 0.091 0.948 0.284 525 0.096 0.974 0.245 530 0.101 1.000 0.206 5350.096 0.998 0.183 540 0.091 0.995 0.159 545 0.088 0.970 0.143 550 0.0850.944 0.126 555 0.090 0.907 0.110 560 0.096 0.870 0.093 565 0.141 0.8250.085 570 0.186 0.780 0.076 575 0.331 0.728 0.073 580 0.476 0.675 0.071585 0.651 0.616 0.070 590 0.826 0.556 0.070 595 0.897 0.485 0.066 6000.968 0.414 0.062 605 0.968 0.354 0.058 610 0.968 0.294 0.053 615 0.9570.255 0.054 620 0.947 0.216 0.055 625 0.932 0.200 0.055 630 0.918 0.1840.055 635 0.899 0.173 0.058 640 0.881 0.161 0.061 645 0.867 0.157 0.067650 0.853 0.152 0.073 655 0.837 0.155 0.078 660 0.822 0.157 0.084 6650.795 0.168 0.087 670 0.767 0.178 0.091 675 0.749 0.196 0.098 680 0.7320.215 0.105 685 0.718 0.237 0.108 690 0.705 0.259 0.111 695 0.704 0.2770.115 700 0.702 0.296 0.119

$\begin{matrix}{{IE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (1) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (2) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (3)\end{matrix}$

TABLE (II) IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range −5 to 5−5 to 5 −5 to 5 0 to 4   IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB)Range −5 to 5 −5 to 5 −5 to 5 0 to 4   IE_(30/40) ^(CR) IE_(30/40) ^(CG)IE_(30/40) ^(CB) Range −3 to 3 −3 to 3 −3 to 3 0 to 1.3

FIG. 2 is a graph showing R(λ), G(λ), and B(λ) shown in Table (I). Thefunctions R(λ), G(λ), and B(λ) were determined as follows. First, 10different commercially-available color image sensors (hereinafter simplyreferred to as “image sensors”) were prepared. These image sensors eachincluded an imaging device such as a charge-coupled device (CCD) orcomplementary metal oxide semiconductor (CMOS) and a color filterconsisting of R (red), G (green) and B (blue) segments. For each imagesensor, spectral sensitivity characteristics for R, G, and B wereavailable as sensitivity spectra with respect to wavelength. For eachimage sensor, the color segment (attribute) having the largest value wasselected from the maximum spectral sensitivity characteristic for R, themaximum spectral sensitivity characteristic for G, and the maximumspectral sensitivity characteristic for B. A coefficient was determinedso that the maximum spectral sensitivity characteristic of the selectedcolor segment was 1, and the spectral sensitivity characteristics for R,the spectral sensitivity characteristics for G, and the spectralsensitivity characteristics for B were multiplied with respect to eachwavelength by the coefficient for normalization. Such operations wereperformed for the spectral sensitivity characteristics of the prepared10 different image sensors to obtain normalized spectral sensitivitycharacteristics of each image sensor. Next, for the normalized spectralsensitivity characteristics of the 10 different image sensors, anarithmetic mean of the spectral sensitivity characteristics for R, thatof the spectral sensitivity characteristics for G, and that of thespectral sensitivity characteristics for B were calculated with respectto each wavelength to determine the average spectral sensitivitycharacteristics for R, G, and B, respectively. The functions R(λ), G(λ),and B(λ) were thus determined.

The normalized spectral sensitivity functions CR_(θ)(λ), CG_(θ)(λ), andCB_(θ)(λ) are determined based on the products of the spectraltransmittance T_(θ)(λ) of the optical filter 1 a and the functions R(λ),G(λ), and B(λ). Afunction determined as a product of the spectraltransmittance T₀(λ) for light incident on the optical filter at anincident angle θ of 0° and R(λ) shown in Table (I), a functiondetermined as a product of T₀(λ) and G(λ), and a function determined asa product of T₀(λ) and B(λ) were calculated. The maximum of eachfunction was determined, and then a coefficient (normalizationcoefficient) was determined so that the largest value of the maximumswas 1. Furthermore, the function determined as the product of thespectral transmittance T₀(λ) and R(λ) shown in Table (I) was multipliedby the normalization coefficient to determine a normalized spectralsensitivity function CR₀(Δλ). In the same manner, normalized spectralsensitivity functions CG₀(λ) and CB₀(λ) were determined. In the samemanner, a function determined as a product of the spectral transmittanceT_(θ)(λ) of the optical filter for light incident on the optical filterat an incident angle of θ° and R(λ) shown in Table (I), a functiondetermined as a product of T_(θ)(λ) and G(λ), and a function determinedas a product of T_(θ)(λ) and B(λ) were respectively multiplied by theabove normalization coefficient to determine the normalized spectralsensitivity functions CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) at an incidentangle of θ°. Here, the products of the spectral transmittance T_(θ)(λ)and the other functions were determined by multiplication thereof withrespect to each wavelength, unless otherwise specified. Therefore, itcan be said that the normalized spectral sensitivity functionsCR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) are functions determined in view ofnot only the characteristics of the optical filter 1 a but also thecharacteristics of a color filter of a camera. A chief ray is incidenton the center of an image sensor or imaging device at an incident angleof almost 0° while incident on the peripheral portion thereof at a largeincident angle. When the shape of a curve of each normalized spectralsensitivity function changes depending on the incident angle of light,color of an image generated by an imaging apparatus is changed at thetime of printing or displaying the image. Therefore, when an image takenby an imaging apparatus is displayed or printed, an object expected tobe colored with one color may gradually discolor from the center towardthe peripheral portion, and the discoloration may be recognized as colorunevenness. Compared to image regions affected by variations in incidentangle of light from 0° to 40° and from 0° to 30°, an image regionaffected by a variation in incident angle of light from 30° to 40° isnarrow. Color unevenness is more easily recognized in the latter region.Therefore, when the shape of the curve of each normalized spectralsensitivity function changes little depending on the variation inincident angle of light, uneven coloring of an image generated by animaging apparatus can be prevented. Since the optical filter 1 asatisfies the requirements shown in Table (II), the shape of the curveof each normalized spectral sensitivity function changes littledepending on the variation in incident angle of light. When an imagingapparatus includes the optical filter 1 a as just described, unevencoloring of an image generated by an imaging apparatus can be prevented.

As shown in the equations (1) to (3), IE_(θ1/θ2) ^(CR), IE_(θ1/θ2)^(CG), and IE_(θ1/θ2) ^(CB) are each determined by integratingdifferences obtained in the wavelength range of 400 nm to 700 nm bysubtracting each of the normalized spectral sensitivity functions at theincident angle θ2° selected from 30° and 40° from the normalizedspectral sensitivity function at the incident angle θ1° (θ1<θ2) selectedfrom 0° and 30°. Therefore, an incident-angle-dependent change in theshape of a curve of each normalized spectral sensitivity function can beevaluated quantitatively by reference to IE_(θ1/θ2) ^(CR), IE_(θ1/θ2)^(CG), and IE_(θ1/θ2) ^(CB).

When an image taken by an imaging apparatus is displayed or printed,correction for optimizing the brightness or color reproduction isperformed for each pixel. Thus, actual spectral sensitivity values arenot directly concerned to this correction. Therefore, thecharacteristics of the optical filter 1 a can be appropriatelydetermined based on the normalized spectral sensitivity functionsCR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) by comparing one and another of thefunctions defined for two different incident angles, as described above.Additionally, because the incident angle of a chief ray incident on eachpixel of an imaging device is predictable, it is conceivable that beforedisplayed or printed, an image taken by an imaging apparatus iscorrected in consideration of a predicted incident angle.

In the optical filter 1 a, IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), andIAE_(θ1/θ2) ^(CB) defined by the following equations (4) to (6) for twoincident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40°desirably satisfy requirements shown in Table (III), and rangesdesirably satisfy requirements shown in Table (III), each range being adifference obtained by subtracting the smallest value of IAE_(θ1/θ2)^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB) defined for the same twoincident angles θ1° and θ2° from the largest value of IAE_(θ1/θ2) ^(CR),IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB) defined for the same twoincident angles θ1° and θ2°.

$\begin{matrix}{{IAE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (4) \\{{IAE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (5) \\{{IAE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (6)\end{matrix}$

TABLE (III) IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 0to 6 0 to 6 0 to 6 0 to 4 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40)^(CB) Range 0 to 6 0 to 6 0 to 6 0 to 4 IAE_(30/40) ^(CR) IAE_(30/40)^(CG) IAE_(30/40) ^(CB) Range 0 to 4 0 to 4 0 to 4   0 to 1.3

As shown in the equations (4) to (6), IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2)^(CG), and IAE_(θ1/θ2) ^(CB) are each determined by integrating theabsolute values of the differences obtained in the wavelength range of400 nm to 700 nm by subtracting the normalized spectral sensitivityfunction at the incident angle θ2° selected from 30° and 40° from thenormalized spectral sensitivity function at the incident angle θ1°(θ1<θ2) selected from 0° and 30°. It may sometimes be difficult toappropriately determine the characteristics of the optical filter onlyby the evaluation using IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), andIE_(θ1/θ2) ^(CB) because the integrated value obtained in a wavelengthband in which differences obtained by subtracting each of the normalizedspectral sensitivity functions at the incident angle θ2° from thenormalized spectral sensitivity function at the incident angle θ1° arenegative can be offset by the integrated value obtained in a differentwavelength band in which differences as described above are positive.When the optical filter 1 a satisfies the requirements shown in Table(III), it is more certain that the shape of a curve of each normalizedspectral sensitivity function changes little depending on the variationin incident angle of light. When an imaging apparatus includes theoptical filter 1 a as just described, uneven coloring of an imagegenerated by an imaging apparatus can be prevented more effectively. Asjust described, the optical filter 1 a can be more appropriatelyevaluated using IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2)^(CB).

In the optical filter 1 a, for example, ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2)^(CG), and ISE_(θ1/θ2) ^(CB) defined by the following equations (7) to(9) for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°,and 40° satisfy requirements shown in Table (IV), and ranges satisfyrequirements shown in Table (IV), each range being a difference obtainedby subtracting the smallest value of ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2)^(CG), and ISE_(θ1/θ2) ^(CB) defined for the same two incident anglesθ1° and θ2° from the largest value of ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2)^(CG), and ISE_(θ1/θ2) ^(CB) defined for the same two incident anglesθ1° and θ20.

$\begin{matrix}{{ISE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (7) \\{{ISE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (8) \\{{ISE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (9)\end{matrix}$

TABLE (IV) ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0 to0.5 0 to 0.5 0 to 0.5 0 to 0.4  ISE_(0/40) ^(CR) ISE_(0/40) ^(CG)ISE_(0/40) ^(CB) Range 0 to 0.5 0 to 0.5 0 to 0.5 0 to 0.4  ISE_(30/40)^(CR) ISE_(30/40) ^(CG) ISE_(30/40) ^(CB) Range 0 to 0.1 0 to 0.1 0 to0.1 0 to 0.08

As shown in the equations (7) to (9), ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2)^(CG), and ISE_(θ1/θ2) ^(CB) are each determined by integrating thesquare values of the differences obtained in the wavelength range of 400nm to 700 nm by subtracting the normalized spectral sensitivity functionat the incident angle θ2° selected from 30° and 40° from the normalizedspectral sensitivity function at the incident angle θ1° (θ1<θ2) selectedfrom 0° and 30°. As described above, it may sometimes be difficult toappropriately determine the characteristics of the optical filter onlyby the evaluation using IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), andIE_(θ1/θ2) ^(CB). When the optical filter 1 a satisfies the requirementsshown in Table (IV), it is more certain that the shape of a curve ofeach normalized spectral sensitivity function changes little dependingon the variation in incident angle of light. When an imaging apparatusincludes the optical filter 1 a as just described, uneven coloring of animage generated by an imaging apparatus can be prevented moreeffectively. As just described, the optical filter 1 a can be moreappropriately evaluated using ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), andISE_(θ1/θ2) ^(CB).

The light absorber included in the light-absorbing layer 10 is notparticularly limited as long as the light absorber absorbs light in atleast a portion of the near-infrared region, the optical filter 1 asatisfies the above requirements (i) to (vii), and the requirementsshown in Table (II) are satisfied. The light absorber is, for example,formed by a phosphonic acid and copper ion. In this case, light in awide wavelength band covering the near-infrared region and a part of thevisible light region adjacent to the near-infrared region can beabsorbed by the light-absorbing layer 10. Therefore, the desiredcharacteristics can be exhibited even when the optical filter 1 a doesnot include a reflecting film. When the optical filter 1 a includes areflecting film, the optical filter 1 a can be designed so that thewavelength band of light reflected by the reflecting film will besufficiently separated apart from the wavelength band of light to betransmitted. For example, the wavelength band of light reflected by thereflecting film can be set 100 nm or more away toward the longwavelength side from the wavelength band of a transition region in whichthe transmittance sharply decreases with increased wavelength. Thus,when the incident angle of light is large and the wavelength band oflight reflected by the reflecting film shifts to the short wavelengthside, the wavelength band of light reflected by the reflecting filmoverlaps with the wavelength band of light absorbed by thelight-absorbing layer 10 and the transmittance characteristics of theoptical filter 1 a in the transition region are unlikely to varydepending on the variation in incident angle of light. Additionally,light in a wide range included in the wavelength band of the ultravioletregion can be absorbed by the light-absorbing layer 10.

When the light-absorbing layer 10 includes the light absorber formed bya phosphonic acid and copper ion, the phosphonic acid includes, forexample, a first phosphonic acid having an aryl group. In the firstphosphonic acid, the aryl group is bonded to a phosphorus atom. Thus,the above requirements are easily satisfied by the optical filter 1 a.

The aryl group of the first phosphonic acid is, for example, a phenylgroup, benzyl group, toluyl group, nitrophenyl group, hydroxyphenylgroup, halogenated phenyl group in which at least one hydrogen atom of aphenyl group is substituted by a halogen atom, or halogenated benzylgroup in which at least one hydrogen atom of a benzene ring of a benzylgroup is substituted by a halogen atom.

When the light-absorbing layer 10 includes the light absorber formed bythe phosphonic acid and copper ion, the phosphonic acid desirablyfurther includes a second phosphonic acid having an alkyl group. In thesecond phosphonic acid, the alkyl group is bonded to a phosphorus atom.

The alkyl group of the second phosphonic acid is, for example, an alkylgroup having 6 or less carbon atoms. This alkyl group may be linear orbranched.

When the light-absorbing layer 10 includes the light absorber formed bythe phosphonic acid and copper ion, the light-absorbing layer 10desirably further includes a phosphoric acid ester allowing the lightabsorber to be dispersed and matrix resin.

The phosphoric acid ester included in the light-absorbing layer 10 isnot limited to any particular one, as long as the phosphoric acid esterallows good dispersion of the light absorber. For example, thephosphoric acid ester includes at least one of a phosphoric acid diesterrepresented by the following formula (c1) and a phosphoric acidmonoester represented by the following formula (c2). In the formulae(c1) and (c2), R₂₁, R₂₂, and R₃ are each a monovalent functional grouprepresented by —(CH₂CH₂O)_(n)R₄, wherein n is an integer of 1 to 25 andR₄ is an alkyl group having 6 to 25 carbon atoms. R₂₁, R₂₂, and R₃ maybe the same or different functional groups.

The phosphoric acid ester is not particularly limited. The phosphoricacid ester can be, for example, PLYSURF A208N (polyoxyethylene alkyl(C12, C13) ether phosphoric acid ester), PLYSURF A208F (polyoxyethylenealkyl (C8) ether phosphoric acid ester), PLYSURF A208B (polyoxyethylenelauryl ether phosphoric acid ester), PLYSURF A219B (polyoxyethylenelauryl ether phosphoric acid ester), PLYSURF AL (polyoxyethylenestyrenated phenylether phosphoric acid ester), PLYSURF A212C(polyoxyethylene tridecyl ether phosphoric acid ester), or PLYSURF A215C(polyoxyethylene tridecyl ether phosphoric acid ester). All of these areproducts manufactured by DKS Co., Ltd. The phosphoric acid ester can beNIKKOL DDP-2 (polyoxyethylene alkyl ether phosphoric acid ester), NIKKOLDDP-4 (polyoxyethylene alkyl ether phosphoric acid ester), or NIKKOLDDP-6 (polyoxyethylene alkyl ether phosphoric acid ester). All of theseare products manufactured by Nikko Chemicals Co., Ltd.

The matrix resin included in the light-absorbing layer 10 is, forexample, a heat-curable or ultraviolet-curable resin in which the lightabsorber is dispersible. Additionally, as the matrix resin can be used aresin that has a transmittance of, for example, 80% or more, preferably85% or more, and more preferably 90% or more for light with a wavelengthof 350 nm to 900 nm in the form of a 0.1-mm-thick resin layer. Thematrix resin is not particularly limited as long as the aboverequirements (i) to (vii) and the requirements shown in Table (II) aresatisfied by the optical filter 1 a. The content of the phosphonic acidin the light-absorbing layer 10 is, for example, 3 to 180 parts by masswith respect to 100 parts by mass of the matrix resin.

The matrix resin included in the light-absorbing layer 10 is notparticularly limited as long as the above characteristics are satisfied.The matrix resin is, for example, a (poly)olefin resin, polyimide resin,polyvinyl butyral resin, polycarbonate resin, polyamide resin,polysulfone resin, polyethersulfone resin, polyamideimide resin,(modified) acrylic resin, epoxy resin, or silicone resin. The matrixresin may contain an aryl group such as a phenyl group and is desirablya silicone resin containing an aryl group such as a phenyl group. If thelight-absorbing layer 10 is excessively hard (rigid), the likelihood ofcure shrinkage-induced cracking during the production process of theoptical filter 1 a increases with increasing thickness of thelight-absorbing layer 10. When the matrix resin is a silicone resincontaining an aryl group, the light-absorbing layer 10 is likely to havehigh crack resistance. Moreover, with the use of a silicone resincontaining an aryl group, the light absorber formed by the abovephosphonic acid and copper ion is less likely to be aggregated whenincluded. Further, when the matrix resin of the light-absorbing layer 10is a silicone resin containing an aryl group, it is desirable for thephosphoric acid ester included in the light-absorbing layer 10 to have aflexible, linear organic functional group, such as an oxyalkyl group,just as does the phosphoric acid ester represented by the formula (c1)or formula (c2). This is because interaction derived from thecombination of the above phosphonic acid, a silicone resin containing anaryl group, and phosphoric acid ester having a linear organic functionalgroup such as an oxyalkyl group makes aggregation of the light absorberless likely and can impart good rigidity and good flexibility to thelight-absorbing layer. Specific examples of the silicone resin availableas the matrix resin include KR-255, KR-300, KR-2621-1, KR-211, KR-311,KR-216, KR-212, and KR-251. All of these are silicone resinsmanufactured by Shin-Etsu Chemical Co., Ltd.

As shown in FIG. 1A, the optical filter 1 a further includes, forexample, a transparent dielectric substrate 20. One principal surface ofthe transparent dielectric substrate 20 is covered with thelight-absorbing layer 10. The characteristics of the transparentdielectric substrate 20 are not particularly limited as long as theabove requirements (i) to (vii) and the requirements shown in Table (II)are satisfied by the optical filter 1 a. The transparent dielectricsubstrate 20 is a dielectric substrate having a high averagetransmittance (for example, 80% or more, preferably 85% or more, andmore preferably 90% or more) in the wavelength range of, for example,450 nm to 600 nm.

The transparent dielectric substrate 20 is, for example, made of glassor resin. When the transparent dielectric substrate 20 is made of glass,the glass is, for example, borosilicate glass such as D 263 T eco,soda-lime glass (blue plate glass), white sheet glass such as B 270,alkali-free glass, or infrared-absorbing glass such as copper-containingphosphate glass or copper-containing fluorophosphate glass. When thetransparent dielectric substrate 20 is made of infrared-absorbing glasssuch as copper-containing phosphate glass or copper-containingfluorophosphate glass, the desired infrared absorption performance canbe imparted to the optical filter 1 a by a combination of the infraredabsorption performance of the transparent dielectric substrate 20 andthe infrared absorption performance of the light-absorbing layer 10.Examples of such an infrared-absorbing glass include BG-60, BG-61,BG-62, BG-63, and BG-67 manufactured by SCHOTT AG, 500EXL manufacturedby Nippon Electric Glass Co., Ltd., and CM5000, CM500, C5000, and C500Smanufactured by HOYA CORPORATION. Moreover, the transparent dielectricsubstrate 20 may have ultraviolet absorption characteristics.

The transparent dielectric substrate 20 may be a transparent crystallinesubstrate, such as magnesium oxide, sapphire, or quartz. For example,sapphire is very hard and is thus scratch resistant. Therefore, as ascratch-resistant protective material (which may be called a protectivefilter or cover glass), a sheet-shaped sapphire is sometimes disposedahead of a camera module or lens included in mobile devices such assmartphones and mobile phones. Formation of the light-absorbing layer 10on such a sheet-shaped sapphire makes it possible to protect cameramodules and lenses and cut off light with a wavelength of 650 nm to 1100nm. This eliminates the need to dispose an optical filter that exhibitsperformance of shielding against infrared light with a wavelength of 650nm to 1100 nm around an imaging device such as a charge-coupled device(CCD) sensor or complementary metal oxide semiconductor (CMOS) sensor orinside a camera module. Therefore, the formation of the light-absorbinglayer 10 on a sheet-shaped sapphire can contribute to achievement oflower-profile camera modules and lower-profile imaging apparatuses.

When the transparent dielectric substrate 20 is made of resin, the resinis, for example, a (poly)olefin resin, polyimide resin, polyvinylbutyral resin, polycarbonate resin, polyamide resin, polysulfone resin,polyethersulfone resin, polyamideimide resin, (modified) acrylic resin,epoxy resin, or silicone resin.

The optical filter 1 a can be produced, for example, by applying acoating liquid for forming the light-absorbing layer 10 to one principalsurface of the transparent dielectric substrate 20 to form a film anddrying the film. The method for preparing the coating liquid and themethod for producing the optical filter 1 a will be described with anexample in which the light-absorbing layer 10 includes the lightabsorber formed by the phosphonic acid and copper ion.

First, an exemplary method for preparing the coating liquid will now bedescribed. A copper salt such as copper acetate monohydrate is added toa given solvent such as tetrahydrofuran (THF), and the mixture isstirred to give a copper salt solution. To this copper salt solution isthen added a phosphoric acid ester compound such as a phosphoric aciddiester represented by the formula (c1) or a phosphoric acid monoesterrepresented by the formula (c2), and the mixture is stirred to prepare asolution A. The first phosphonic acid is added to a given solvent suchas THF, and the mixture is stirred to prepare a solution B. Next, thesolution B is added to the solution A while the solution A is stirred,and the mixture is further stirred for a given period of time. To theresultant solution is then added a given solvent such as toluene, andthe mixture is stirred to obtain a solution C. Subsequently, thesolution C is subjected to solvent removal under heating for a givenperiod of time to obtain a solution D. This process removes the solventsuch as THF and the component such as acetic acid (boiling point: about118° C.) generated by disassociation of the copper salt and yields alight absorber formed by the first phosphonic acid and copper ion. Thetemperature at which the solution C is heated is chosen based on theboiling point of the to-be-removed component disassociated from thecopper salt. During the solvent removal, the solvent such as toluene(boiling point: about 110° C.) used to obtain the solution C is alsoevaporated. A certain amount of this solvent desirably remains in thecoating liquid. This is preferably taken into account in determining theamount of the solvent to be added and the time period of the solventremoval. To obtain the solution C, o-xylene (boiling point: about 144°C.) may be used instead of toluene. In this case, the amount of o-xyleneto be added can be reduced to about one-fourth of the amount of tolueneto be added, because the boiling point of o-xylene is higher than theboiling point of toluene. A matrix resin such as a silicone resin isadded to the solution D and the mixture is stirred. The coating liquidcan thus be prepared.

The coating liquid is applied to one principal surface of thetransparent dielectric substrate 20 to form a film. For example, thecoating liquid is applied to one principal surface of the transparentdielectric substrate 20 by die coating or spin coating or with adispenser to form a film. Next, this film is cured by a given heattreatment. For example, the film is exposed to an environment at atemperature of 50° C. to 200° C. for a given period of time.

In the optical filter 1 a, the light-absorbing layer 10 may be formed asa single layer or may be formed as a plurality of layers. When thelight-absorbing layer 10 is formed as a plurality of layers, thelight-absorbing layer 10 includes, for example, a first layer includingthe light absorber formed by the first phosphonic acid and copper ionand a second layer including the light absorber formed by the secondphosphonic acid and copper ion. In this case, a coating liquid forforming the first layer can be prepared in the above manner. The secondlayer is formed using a coating liquid prepared separately from thecoating liquid for forming the first layer. The coating liquid forforming the second layer can be prepared, for example, in the followingmanner.

A copper salt such as copper acetate monohydrate is added to a givensolvent such as tetrahydrofuran (THF), and the mixture is stirred togive a copper salt solution. To this copper salt solution is then addeda phosphoric acid ester compound such as a phosphoric acid diesterrepresented by the formula (c1) or a phosphoric acid monoesterrepresented by the formula (c2), and the mixture is stirred to prepare asolution E. The second phosphonic acid is added to a given solvent suchas THF, and the mixture is stirred to prepare a solution F. Next, thesolution F is added to the solution E while the solution E is stirred,and the mixture is further stirred for a given period of time. To theresultant solution is then added a given solvent such as toluene, andthe mixture is stirred. The solvent is evaporated to obtain a solutionG. Subsequently, a matrix resin such as a silicone resin is added to thesolution G, and the mixture is stirred. The coating liquid for formingthe second layer can thus be obtained.

The first and second layers can be formed by applying the coating liquidfor forming the first layer and that for forming the second layer toform films, which are cured by a given heat treatment. For example, thefilms are exposed to an environment at a temperature of 50° C. to 200°C. for a given period of time. The order of forming the first and secondlayers is not particularly limited. The first and second layers may beformed in different time periods, or may be formed in the same timeperiod. A protective layer may be formed between the first and secondlayers. The protective layer is formed of, for example, a SiO₂-depositedfilm.

<Modifications>

The optical filter 1 a can be modified in various respects. For example,the optical filter 1 a may be modified to optical filters 1 b to 1 fshown in FIG. 1B to FIG. 1F. The optical filters 1 b to 1 f areconfigured in the same manner as the optical filter 1 a, unlessotherwise described. The components of the optical filters 1 b to 1 fthat are the same as or correspond to those of the optical filter 1 aare denoted by the same reference characters, and detailed descriptionsof such components are omitted. The description given for the opticalfilter 1 a can apply to the optical filters 1 b to 1 f, unless there istechnical inconsistency.

As shown in FIG. 1B, the optical filter 1 b has the light-absorbinglayers 10 formed on both principal surfaces of the transparentdielectric substrate 20. Therefore, the above requirements (i) to (vii)and the requirements shown in Table (II) are satisfied by the twolight-absorbing layers 10 rather than one light-absorbing layer 10. Thelight-absorbing layers 10 on both principal surfaces of the transparentdielectric substrate 20 may have the same or different thicknesses. Thatis, the formation of the light-absorbing layers 10 on both principalsurfaces of the transparent dielectric substrate 20 is done so that thetwo light-absorbing layers 10 account for equal or unequal proportionsof the light-absorbing layer thickness required for the optical filter 1b to have desired optical characteristics. Thus, each of thelight-absorbing layers 10 formed on both principal surfaces of thetransparent dielectric substrate 20 of the optical filter 1 b has asmaller thickness than the thickness of the light-absorbing layer 10 ofthe optical filter 1 a. The formation of the light-absorbing layers 10on both principal surfaces of the transparent dielectric substrate 20can reduce warping of the optical filter 1 b even when the transparentdielectric substrate 20 is thin. Each of the two light-absorbing layers10 may be formed as a plurality of layers.

As shown in FIG. 1C, the optical filter 1 c has the light-absorbinglayers 10 formed on both principal surfaces of the transparentdielectric substrate 20. The optical filter 1 e additionally includes ananti-reflection film 30. The anti-reflection film 30 is a film formed asan interface between the optical filter 1 e and air and reducingreflection of visible light. The anti-reflection film 30 is, forexample, a film formed of a dielectric made of, for example, a resin, anoxide, or a fluoride. The anti-reflection film 30 may be a multilayerfilm formed by laminating two or more types of dielectrics havingdifferent refractive indices. The anti-reflection film 30 may be,particularly, a dielectric multilayer film made of alow-refractive-index material such as SiO₂ and a high-refractive-indexmaterial such as TiO₂ or Ta₂O₅. In this case, Fresnel reflection at theinterface between the optical filter 1 e and air is reduced and theamount of visible light transmitted through the optical filter 1 e canbe increased. The anti-reflection film 30 may be formed on both sides ofthe optical filter 1 c, or may be formed on one side thereof.

As shown in FIG. 1D, the optical filter 1 d has the light-absorbinglayers 10 formed on both principal surfaces of the transparentdielectric substrate 20. Additionally, the optical filter 1 d furtherincludes a reflecting film 40. The reflecting film 40 reflects infraredlight and/or ultraviolet light. The reflecting film 40 is, for example,a film formed by vapor deposition of a metal such as aluminum or adielectric multilayer film in which a layer formed of ahigh-refractive-index material and a layer formed of alow-refractive-index material are alternately laminated. A material,such as TiO₂, ZrO₂, Ta₂O₅, Nb₂O₅, ZnO, or In₂O₃, having a refractiveindex of 1.7 to 2.5 is used as the high-refractive-index material. Amaterial, such as SiO₂, Al₂O₃, or MgF₂, having a refractive index of 1.2to 1.6 is used as the low-refractive-index material. Examples of themethod for forming the dielectric multilayer film include chemical vapordeposition (CVD), sputtering, and vacuum deposition. Such reflectingfilms may be formed to be both principal surfaces of the optical filter(not shown). The reflecting films formed on both principal surfaces ofthe optical filter balance the stress on the front side and that on theback side, and that offers an advantage of decreasing the likelihood ofwarping of the optical filter.

As shown in FIG. 1E, the optical filter 1 e consists only of thelight-absorbing layer 10. The optical filter 1 e can be produced, forexample, by applying the coating liquid onto a given substrate such as aglass substrate, resin substrate, or metal substrate (such as a steelsubstrate or stainless steel substrate) to form a film, curing the film,and then separating the film from the substrate. The optical filter 1 emay be produced by casting. Not including the transparent dielectricsubstrate 20, the optical filter 1 e is thin. The optical filter 1 e canthus contribute to achievement of lower-profile imaging apparatuses.

As shown in FIG. 1F, the optical filter if includes the light-absorbinglayer 10 and a pair of the anti-reflection films 30 disposed on bothsides of the light-absorbing layer 10. In this case, the optical filterif can contribute to achievement of lower-profile imaging apparatuses,and can increase the amount of visible light transmitted therethroughmore than the optical filter 1 e can.

The optical filters 1 a to 1 f may be modified to include aninfrared-absorbing layer (not shown) in addition to the light-absorbinglayer 10, if necessary. The infrared-absorbing layer includes, forexample, an organic infrared absorber, such as a cyanine-based,phthalocyanine-based, squarylium-based, diimmonium-based, or azo-basedinfrared absorber or an infrared absorber composed of a metal complex.The infrared-absorbing layer includes, for example, one infraredabsorber or two or more infrared absorbers selected from these infraredabsorbers. The organic infrared absorber can absorb light in arelatively narrow wavelength range (absorption band) and is suitable forabsorbing light with a given wavelength range.

The optical filters 1 a to if may be modified to include anultraviolet-absorbing layer (not shown) in addition to thelight-absorbing layer 10, if necessary. The ultraviolet-absorbing layerincludes, for example, an ultraviolet absorber, such as abenzophenone-based, triazine-based, indole-based, merocyanine-based, oroxazole-based ultraviolet absorber. The ultraviolet-absorbing layer, forexample, includes one ultraviolet absorber or two or more ultravioletabsorbers selected from these ultraviolet absorbers. The ultravioletabsorber can include ultraviolet absorbers absorbing ultraviolet lightaround a wavelength of, for example, 300 nm to 340 nm, emitting light(fluorescence) with a wavelength longer than the absorbed wavelength,and functioning as a fluorescent agent or fluorescent brightener. Theultraviolet-absorbing layer can reduce incidence of ultraviolet lightwhich deteriorates the materials, such as resin, used in the opticalfilter.

The above infrared absorber and/or ultraviolet absorber may be containedbeforehand in the transparent dielectric substrate 20 made of resin toform a substrate having characteristics of absorbing infrared lightand/or ultraviolet light. In this case, it is necessary for the resin toallow the infrared absorber and/or ultraviolet absorber to beappropriately dissolved or dispersed therein and be transparent.Examples of such a resin include a (poly)olefin resin, polyimide resin,polyvinyl butyral resin, polycarbonate resin, polyamide resin,polysulfone resin, polyethersulfone resin, polyamideimide resin,(modified) acrylic resin, epoxy resin, and silicone resin.

As shown in FIG. 3, the optical filter 1 a is used to produce, forexample, an imaging apparatus 100 (camera module). The imaging apparatus100 includes a lens system 2, an imaging device 4, a color filter 3, andthe optical filter 1 a. The imaging device 4 receives light having beentransmitted through the lens system 2. The color filter 3 is disposedahead of the imaging device 4 and is a filter of three colors, R (red),G (green), and B (blue). The optical filter 1 a is disposed ahead of thecolor filter 3. The light-absorbing layer 10 is particularly arranged tobe in contact with a side of the transparent dielectric substrate 20,the side being closer to the lens system 2. As described previously, theprotecting effect on the lens system 2 or imaging device 4 increaseswhen a hard material such as sapphire is used as the transparentdielectric substrate 20. For example, in the color filter 3, the threecolors, R (red), G (green), and B (blue), are arranged in a matrix, andeach of the R (red), G (green), and B (blue) colors is disposedimmediately above a pixel of the imaging device 4. The imaging device 4receives light coming from an object and having been transmitted throughthe lens system 2, optical filter 1 a, and color filter 3. The imagingapparatus 100 generates an image based on information on electric chargeproduced by the light received by the imaging device 4. The color filter3 and imaging device 4 may be combined to configure a color imagesensor.

The above requirements (i) to (vii) and the requirements shown in Table(II) are satisfied by the optical filter 1 a. The imaging apparatus 100including the optical filter 1 a can therefore generate images unevencoloring of which is prevented.

EXAMPLES

The present invention will be described in more detail by examples. Thepresent invention is not limited to the examples given below.

<Measurement of Transmittance Spectra>

Transmittance spectra shown upon incidence of light with wavelengths of300 nm to 1200 nm on optical filters according to Examples andComparative Examples, intermediate products thereof, and laminatesaccording to Reference Examples were measured using anultraviolet-visible spectrophotometer (manufactured by JASCOCorporation, product name: V-670). The incident angle of light incidenton the optical filters of Examples and Comparative Examples, some of theintermediate products thereof, and some of the laminates according toReference Examples was set to 0°, 30°, and 400 to measure thetransmittance spectra thereof. The incident angle of light incident onthe other intermediate products and the other laminates according toReference Examples was set to 0° to measure the transmittance spectrathereof.

Example 1

A coating liquid IRA1 was prepared in the following manner. 1.1 g ofcopper acetate monohydrate and 60 g of tetrahydrofuran (THF) were mixed,followed by stirring for 3 hours. To the obtained solution was added 2.3g of a phosphoric acid ester (manufactured by DKS Co., Ltd., productname: PLYSURF A208F), followed by stirring for 30 minutes to obtain asolution A. 10 g of THF was added to 0.6 g of phenylphosphonic acid(manufactured by Tokyo Chemical Industry Co., Ltd.), followed bystirring for 30 minutes to obtain a solution B. The solution B was addedto the solution A while the solution A was stirred, and the mixture wasstirred at room temperature for 1 minute. To the resultant solution wasadded 45 g of toluene, followed by stirring at room temperature for 1minute to obtain a solution C. The solution C was placed in a flask andsubjected to solvent removal for 25 minutes using a rotary evaporator(manufactured by Tokyo Rikakikai Co., Ltd., product code: N-1110SF)under heating by means of an oil bath (manufactured by Tokyo RikakikaiCo., Ltd., product code: OSB-2100) controlled to 120° C. A solution Dwas thus obtained. The solution D was taken out of the flask, and to thesolution D was added 4.4 g of a silicone resin (manufactured byShin-Etsu Chemical Co., Ltd., product name: KR-300), followed bystirring at room temperature for 30 minutes to obtain a coating liquidIRA1.

A coating liquid IRA2 was prepared in the following manner. 2.25 g ofcopper acetate monohydrate and 120 g of tetrahydrofuran (THF) weremixed, followed by stirring for 3 hours. To the obtained solution wasadded 1.8 g of a phosphoric acid ester (manufactured by DKS Co., Ltd.,product name: PLYSURF A208F), followed by stirring for 30 minutes toobtain a solution E. 20 g of THF was added to 1.35 g of butylphosphonicacid, followed by stirring for 30 minutes to obtain a solution F. Thesolution F was added to the solution E while the solution E was stirred,and the mixture was stirred at room temperature for 3 hours. To theresultant solution was added 40 g of toluene, and the solvent wasevaporated in an 85° C. environment over 7.5 hours to obtain a solutionG. To the solution G was added 8.8 g of a silicone resin (manufacturedby Shin-Etsu Chemical Co., Ltd., product name: KR-300), followed bystirring for 3 hours to obtain a solution IRA2.

The coating liquid IRA1 was applied to one principal surface of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) using a die coater. The resultant film was cured by heattreatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. Anintermediate product α of an optical filter according to Example 1 wasthus obtained. The total thickness of the infrared-absorbing layer ira11and infrared-absorbing layer ira12 is 0.2 mm. A transmittance spectrumshown by the intermediate product α at an incident angle of 0° is shownin FIG. 4A. The intermediate product α has the following characteristics(α1) to (A6).

(α1): The average transmittance in the wavelength range of 700 to 1000nm is 0.5% or less.

(α2): The average transmittance in the wavelength range of 1100 to 1200nm is 29.5%.

(α3): The average transmittance in the wavelength range of 450 to 600 nmis 88.0%.

(α4): The transmittance at a wavelength of 400 nm is 63.7%.

(α5): The IR cut-off wavelength is 632 nm, the UV cut-off wavelength is394 nm, and when the difference between the IR cut-off wavelength and UVcut-off wavelength is regarded as a full width at half maximum in atransmission region, the full width at half maximum in the transmissionregion is 238 nm.

(α6): The wavelength which lies in the wavelength range of 600 to 800 nmand at which the spectral transmittance is 20% is 661 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed onthe infrared-absorbing layer ira11 of the intermediate product α using avacuum deposition apparatus. In the same manner, a 500-nm-thickSiO₂-deposited film (protective layer p2) was formed on theinfrared-absorbing layer ira12 of the intermediate product α. Thecoating liquid IRA2 was applied to the surface of the protective layerp1 with a die coater. The resultant film was cured by heat treatment inan oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1hour, and then at 170° C. for 3 hours to form an infrared-absorbinglayer ira21. The coating liquid IRA2 was applied also to the surface ofthe protective layer p2 with a die coater. The resultant film was curedunder the same heating conditions to form an infrared-absorbing layerira22. An intermediate product ß was thus obtained. The total thicknessof the infrared-absorbing layer ira21 and infrared-absorbing layer ira22is 50 μm. A transmittance spectrum of the intermediate product ß isshown in FIG. 4B. The intermediate product ß has the followingcharacteristics (ß1) to (ß6).

(ß1): The average transmittance in the wavelength range of 700 to 1000nm is 0.5% or less.

(ß2): The average transmittance in the wavelength of 1100 to 1200 nm is4.5%.

(ß3): The average transmittance in the wavelength range of 450 to 600 nmis 86.9%.

(ß4): The transmittance at a wavelength of 400 nm is 62.1%.

(ß5): The IR cut-off wavelength is 631 nm, the UV cut-off wavelength is394 nm, and the full width at half maximum of the transmission region is237 nm.

(ß6): The wavelength which lies in the wavelength range of 600 to 800 nmand at which the spectral transmittance is 20% is 659 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p3) was formed onthe infrared-absorbing layer ira22 of the intermediate product ß using avacuum deposition apparatus.

A coating liquid UVA1 was prepared in the following manner. Abenzophenone-based ultraviolet-absorbing substance having low lightabsorption in the visible region and soluble in methyl ethyl ketone(MEK) was used as an ultraviolet-absorbing substance. Thisultraviolet-absorbing substance was dissolved in MEK serving as asolvent, to which polyvinyl butyral (PVB) in which the solids accountfor 60 weight % was added, followed by stirring for 2 hours to obtain acoating liquid UVA1. The coating liquid UVA1 was applied onto theprotective layer p3 by spin coating, followed by curing by heating at140° C. for 30 minutes to form an ultraviolet-absorbing layer uva1. Thethickness of the ultraviolet-absorbing layer uva1 is 6 μm. Separately, alaminate according to Reference Example 1 was obtained by forming a6-μm-thick ultraviolet-absorbing layer on a surface of a transparentglass substrate (manufactured by SCHOTT AG, product name: D 263 T eco)using the coating liquid UVA1 by spin coating. A transmittance spectrumof the laminate according to Reference Example 1 is shown in FIG. 4C.The laminate according to Reference Example 1 has the followingcharacteristics (r1) to (r3).

(r1): The transmittance in the wavelength range of 350 to 390 nm is 0.5%or less.

(r2): The transmittance at a wavelength of 400 nm is 12.9%, thetransmittance at a wavelength of 410 nm is 51.8%, the transmittance at awavelength of 420 nm is 77.1%, and the transmittance at a wavelength of450 nm is 89.8%.

(r3): The average transmittance in the wavelength range of 450 to 750 nmis 91.0%.

An anti-reflection film ar1 was formed on the infrared-absorbing layerira21 using a vacuum deposition apparatus. An anti-reflection film ar2was formed on the ultraviolet-absorbing layer uva1 using a vacuumdeposition apparatus. The specifications of the anti-reflection film ar1and anti-reflection film ar2 are the same. Each of the anti-reflectionfilm ar1 and anti-reflection film ar2 is a film composed of SiO₂ andTiO₂ that are alternately laminated, includes 7 layers, and has a totalthickness of about 0.4 μm. An optical filter according to Example 1 wasthus obtained. An anti-reflection film was formed on one side of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) under the same conditions as for the formation of theanti-reflection film ar1 to obtain a laminate according to ReferenceExample 2. Transmittance spectra of the laminate according to ReferenceExample 2 are shown in FIG. 4D. The laminate according to ReferenceExample 2 has the following characteristics (s1) to (s4).

(s1): When the incident angle of light is 0°, the transmittance at awavelength of 350 nm is 73.4%, the transmittance at a wavelength of 380nm is 88.9%, the transmittance at a wavelength of 400 nm is 95.3%, theaverage transmittance in the wavelength range of 400 to 700 nm is 95.3%,and the transmittance at a wavelength of 715 nm is 95.7%.

(s2): When the incident angle of light is 30°, the transmittance at awavelength of 350 nm is 78.5%, the transmittance at a wavelength of 380nm is 92.0%, the transmittance at a wavelength of 400 nm is 94.5%, theaverage transmittance in the wavelength range of 400 to 700 nm is 94.3%,and the transmittance at a wavelength of 715 nm is 94.6%.

(s3): When the incident angle of light is 40°, the transmittance at awavelength of 350 nm is 82.3%, the transmittance at a wavelength of 380nm is 93.3%, the transmittance at a wavelength of 400 nm is 94.3%, theaverage transmittance in the wavelength range of 400 to 700 nm is 94.0%,and the transmittance at a wavelength of 715 nm is 94.1%.

(s4): In the wavelength range of 400 to 700 nm, there is no wavelengthband in which a ripple, i.e., a local decrease in transmittance, occurs,regardless of the incident angle of light.

Transmittance spectra of the optical filter according to Example 1 areshown in FIG. 4E and Table 7. The optical filter according to Example 1has the characteristics shown in Table 8. A function determined as aproduct of the spectral transmittance T₀(λ) of the optical filter forlight incident on the optical filter at an incident angle θ of 0° andR(λ) shown in Table (I), a function determined as a product of T₀(λ) andG(λ), and a function determined as a product of T₀(and B(λ) werecalculated. Next, the maximum of each function was determined, and thena normalization coefficient was determined so that the largest value ofthe maximums was 1. Furthermore, the function determined as the productof the spectral transmittance T₀(λ) and R(λ) shown in Table (I) wasmultiplied by the normalization coefficient to determine a normalizedspectral sensitivity function CR₀(λ). In the same manner, normalizedspectral sensitivity functions CG₀(λ) and CB₀(λ) were determined. Afunction determined as a product of the spectral transmittance T₃₀(λ) ofthe optical filter for light incident on the optical filter at anincident angle of 30° and R(λ) shown in Table (I), a function determinedas a product of T₃₀(λ) and G(λ), and a function determined as a productof T₃₀(λ) and B(λ) were respectively multiplied by the normalizationcoefficient to determine normalized spectral sensitivity functionsCR₃₀(λ), CG₃₀(λ), and CB₃₀(λ) at an incident angle of 30°. A functiondetermined as a product of the spectral transmittance T₄₀(λ) of theoptical filter for light incident on the optical filter at an incidentangle of 40° and R(λ) shown in Table (I), a function determined as aproduct of T₄₀(λ) and G(λ), and a function determined as a product ofT₄₀(λ) and B(λ) were respectively multiplied by the normalizationcoefficient to determine normalized spectral sensitivity functionsCR₄₀(λ), CG₄₀(λ), and CB₄₀(λ) at an incident angle of 30°. FIG. 5A, FIG.5B, and FIG. 5C show the normalized spectral sensitivity functionsdetermined for light incident on the optical filter at incident angle θof 0°, 30°, and 40°. FIG. 6A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functionsdetermined for light incident on the optical filter at an incident angleθ of 30° from the normalized spectral sensitivity function determinedfor light incident thereon at an incident angle θ of 0°. FIG. 6B is agraph showing differences obtained by subtracting each of the normalizedspectral sensitivity functions at an incident angle θ of 40° from thenormalized spectral sensitivity function at an incident angle θ of 0°.FIG. 6C is a graph showing differences obtained by subtracting each ofthe normalized spectral sensitivity functions at an incident angle θ of40° from the normalized spectral sensitivity function at an incidentangle θ of 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2)^(CB); IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); andISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) weredetermined by the above equations (1) to (9) using the normalizedspectral sensitivity functions determined for two incident angles θ1°and θ2° (θ1<θ2) selected from 0°, 30°, and 40°. Tables 9 to 11 show theresults.

Example 2

Coating liquids IRA1 and IRA2 were prepared in the same manner as inExample 1. The coating liquid IRA1 was applied to one principal surfaceof a transparent glass substrate (manufactured by SCHOTT AG, productname: D 263 T eco) using a die coater. The resultant film was cured byheat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours,at 150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. The totalthickness of the infrared-absorbing layer ira11 and infrared-absorbinglayer ira12 is 0.2 mm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed onthe infrared-absorbing layer ira11 using a vacuum deposition apparatus.In the same manner, a 500-nm-thick SiO₂-deposited film (protective layerp2) was formed on the infrared-absorbing layer ira12. The coating liquidIRA2 was applied to the surface of the protective layer p1 with a diecoater. The resultant film was cured by heat treatment in an oven at 85°C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and thenat 170° C. for 3 hours to form an infrared-absorbing layer ira21. Thecoating liquid IRA2 was applied also to the surface of the protectivelayer p2 with a die coater. The resultant film was cured under the sameheating conditions to form an infrared-absorbing layer ira22. The totalthickness of the infrared-absorbing layer ira21 and infrared-absorbinglayer ira22 is 50 μm.

A 500-nm-thick SiO₂-deposited film (protective layer p3) was formed onthe infrared-absorbing layer ira22 using a vacuum deposition apparatus.A coating liquid UVIRA1 containing an infrared-absorbing dye andultraviolet-absorbing dye was prepared in the following manner. Theinfrared-absorbing dye is a combination of a cyanine-based organic dyeand squarylium-based organic dye, has an absorption peak in thewavelength range of 680 to 780 nm, and is less likely to absorb light inthe visible region. The ultraviolet-absorbing dye is a dye composed of abenzophenone-based ultraviolet-absorbing substance which is less likelyto absorb light in the visible region. The infrared-absorbing dye andultraviolet-absorbing dye are soluble in MEK. The infrared-absorbing dyeand ultraviolet-absorbing dye were added to MEK serving as a solvent,and PVB serving as a matrix was also added thereto, followed by stirringfor 2 hours to obtain a coating liquid UVIRA1. The content of theinfrared-absorbing dye and the content of the ultraviolet-absorbing dyein the coating liquid UVIRA1 were determined so that a laminateaccording to Reference Example 3 would show a transmittance spectrum asshown in FIG. 7A. The laminate according to Reference Example 3 wasproduced by applying the coating liquid UVIRA1 onto a transparent glasssubstrate (manufactured by SCHOTT AG, product name: D 263 T eco) by spincoating, and curing the resultant film by heating at 140° C. for 30minutes. In the coating liquid UVIRA1, the mass ratio (mass ofinfrared-absorbing dye:mass of solids of PVB) between theinfrared-absorbing dye and the solids of PVB is about 1:199. The massratio (mass of ultraviolet-absorbing dye:mass of solids of PVB) betweenthe ultraviolet-absorbing dye and the solids of PVB is about 40:60. Thelaminate according to Reference Example 3 has the followingcharacteristics (t1) to (t5).

(t1): The transmittance at a wavelength of 700 nm is 8.7%, thetransmittance at a wavelength of 715 nm is 13.6%, and the averagetransmittance in the wavelength range of 700 to 800 nm is 66.2%.

(t2): The transmittance at a wavelength of 1100 nm is 92.1%.

(t3): The transmittance at a wavelength of 400 nm is 11.8%, thetransmittance at a wavelength of 450 nm is 85.3%, and the averagetransmittance in the wavelength range of 500 to 600 nm is 89.1%.

(t4): The IR cut-off wavelength in the wavelength range of 600 nm to 700nm is 669 nm, the IR cut-off wavelength in the wavelength range of 700nm to 800 nm is 729 nm, and the difference therebetween is 60 nm. Thewavelength (wavelength of maximum absorption) at which the transmittanceis the lowest in the wavelength range of 600 nm to 800 nm is 705 nm.

(t5): The UV cut-off wavelength in the wavelength range of 350 nm to 450nm is 411 nm.

The coating liquid UVIRA1 was applied onto the protective layer p3 byspin coating, and the resultant film was cured by heating at 140° C. for30 minutes to form an infrared- and ultraviolet-absorbing layer uvira1.The thickness of the infrared- and ultraviolet-absorbing layer uvira1 is7 μm.

An anti-reflection film ar1 was formed on the infrared-absorbing layerira21 using a vacuum deposition apparatus. An anti-reflection film ar2was formed on the infrared- and ultraviolet-absorbing layer uvira1 usinga vacuum deposition apparatus. The specifications of the anti-reflectionfilm ar1 and anti-reflection film ar2 are the same. Each of theanti-reflection film ar1 and anti-reflection film ar2 is a film composedof SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, andhas a total thickness of about 0.4 μm. An optical filter according toExample 2 was thus obtained.

Transmittance spectra of the optical filter according to Example 2 areshown in FIG. 7B and Table 12. The optical filter according to Example 2has the characteristics shown in Table 13. In the same manner as inExample 1, the normalized spectral sensitivity functions CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ) were determined based on the spectraltransmittance T_(θ)(λ) shown by the optical filter according to Example2 for light incident at incident angles θ of 0°, 30°, and 40° and R(λ),G(λ), and B(λ) shown in Table (I). FIG. 8A, FIG. 8B, and FIG. 8C showthe normalized spectral sensitivity functions at incident angle θ of 0°,30°, and 40°. FIG. 9A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functions at anincident angle θ of 30° from the normalized spectral sensitivityfunction at an incident angle θ of 0°. FIG. 9B is a graph showingdifferences obtained by subtracting each of the normalized spectralsensitivity functions at an incident angle θ of 40° from the normalizedspectral sensitivity function at an incident angle θ of 0°. FIG. 9C is agraph showing differences obtained by subtracting each of the normalizedspectral sensitivity functions at an incident angle θ of 40° from thenormalized spectral sensitivity function at an incident angle θ of 30°.IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB); IAE_(θ1/θ2)^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); and ISE_(θ1/θ2) ^(CR),ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) were determined by the aboveequations (1) to (9) using the normalized spectral sensitivity functionsdetermined for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°,30°, and 40°. Tables 14 to 16 show the results.

Example 3

Coating liquids IRA1 and IRA2 were prepared in the same manner as inExample 1. The coating liquid IRA1 was applied to one principal surfaceof a transparent glass substrate (manufactured by SCHOTT AG, productname: D 263 T eco) using a die coater. The resultant film was cured byheat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours,at 150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. Anintermediate product γ of an optical filter according to Example 3 wasthus obtained. The total thickness of the infrared-absorbing layer ira11and infrared-absorbing layer ira12 is 0.2 mm. A transmittance spectrumshown by the intermediate product γ at an incident angle of 0° is shownin FIG. 10A. The intermediate product γ has the followingcharacteristics (γ1) to (γ6).

(γ1): The average transmittance in the wavelength range of 700 to 1000nm is 0.5% or less.

(γ2): The average transmittance in the wavelength range of 1100 to 1200nm is 25.9%.

(γ3): The average transmittance in the wavelength range of 450 to 600 nmis 87.5%.

(γ4): The transmittance at a wavelength of 400 nm is 60.9%.

(γ5): The IR cut-off wavelength is 629 nm, the UV cut-off wavelength is395 nm, and the full width at half maximum in the transmission region is234 nm.

(γ6): The wavelength which lies in the wavelength range of 600 to 800 nmand at which the spectral transmittance is 20% is 657 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed onthe infrared-absorbing layer ira12 of the intermediate product γ. Acoating liquid UVA1 as used in Example 1 was applied onto the protectivelayer p2 by spin coating and the resultant film was cured by heating at140° C. for 30 minutes to form an ultraviolet-absorbing layer uva1. Thethickness of the ultraviolet-absorbing layer uva1 is 6 μm.

An anti-reflection film ar1 was formed on the infrared-absorbing layerira11 using a vacuum deposition apparatus. An anti-reflection film ar2was formed on the ultraviolet-absorbing layer uva1 using a vacuumdeposition apparatus. The specifications of the anti-reflection film ar1and anti-reflection film ar2 are the same. Each of the anti-reflectionfilm ar1 and anti-reflection film ar2 is a film composed of SiO₂ andTiO₂ that are alternately laminated, includes 7 layers, and has a totalthickness of about 0.4 μm. An optical filter according to Example 3 wasthus obtained.

Transmittance spectra of the optical filter according to Example 3 areshown in FIG. 10B and Table 17. The optical filter according to Example3 has the characteristics shown in Table 18. In the same manner as inExample 1, the normalized spectral sensitivity functions CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ) were determined based on the spectraltransmittance T_(θ)(λ) shown by the optical filter according to Example3 for light incident at incident angles θ of 0°, 30°, and 400 and R(λ),G(λ), and B(λ) shown in Table (I). FIG. 11A, FIG. 11B, and FIG. 11C showthe normalized spectral sensitivity functions at incident angle θ of 0°,30°, and 40°. FIG. 12A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functions at anincident angle θ of 30° from the normalized spectral sensitivityfunction at an incident angle θ of θ°0. FIG. 12B is a graph showingdifferences obtained by subtracting each of the normalized spectralsensitivity functions at an incident angle θ of 40° from the normalizedspectral sensitivity function at an incident angle θ of 0°. FIG. 12C isa graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 40°from the normalized spectral sensitivity function at an incident angle θof 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB);IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); andISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) weredetermined by the above equations (1) to (9) using the normalizedspectral sensitivity functions determined for two incident angles θ1°and θ2° (θ1<θ2) selected from 0°, 30°, and 40°. Tables 19 to 21 show theresults.

Example 4

A coating liquid IRA1 was prepared in the same manner as in Example 1.The coating liquid IRA1 was applied to one principal surface of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) using a die coater. The resultant film was cured by heattreatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. The totalthickness of the infrared-absorbing layer ira11 and infrared-absorbinglayer ira12 is 0.2 mm.

Next, an infrared-reflecting film irr1 was formed on theinfrared-absorbing layer ira11 using a vacuum deposition apparatus. Theinfrared-reflecting film irr1 is composed of SiO₂ and TiO₂ that arealternately laminated in 16 layers. An infrared-reflecting film wasformed on one principal surface of a transparent glass substrate(manufactured by SCHOTT AG, product name: D 263 T eco) under the sameconditions as for the formation of the infrared-reflecting film irr1 toproduce a laminate according to Reference Example 4. Transmittancespectra of the laminate according to Reference Example 4 are shown inFIG. 13A. The laminate according to Reference Example 4 has thefollowing characteristics (u1) to (u3).

(u1): When the incident angle of light is 0°, the transmittance at awavelength of 380 nm is 1.8%, the transmittance at a wavelength of 400nm is 7.3%, the average transmittance in the wavelength range of 450 to700 nm is 94.8%, the lowest transmittance in the wavelength range of 450to 700 nm is 93.4%, the average transmittance in the wavelength range of700 to 800 nm is 94.0%, the transmittance at a wavelength of 1100 nm is4.1%, the IR cut-off wavelength is 902 nm, and the UV cut-off wavelengthis 410 nm.

(u2): When the incident angle of light is 30°, the transmittance at awavelength of 380 nm is 1.8%, the transmittance at a wavelength of 400nm is 67.8%, the average transmittance in the wavelength range of 450 to700 nm is 95.0%, the lowest transmittance in the wavelength range of 450to 700 nm is 93.8%, the average transmittance in the wavelength range of700 to 800 nm is 92.1%, the transmittance at a wavelength of 1100 nm is5.3%, the IR cut-off wavelength is 863 nm, and the UV cut-off wavelengthis 398 nm.

(u3): When the incident angle of light is 40°, the transmittance at awavelength of 380 nm is 4.0%, the transmittance at a wavelength of 400nm is 90.2%, the average transmittance in the wavelength range of 450 to700 nm is 94.1%, the lowest transmittance in the wavelength range of 450to 700 nm is 92.9%, the average transmittance in the wavelength range of700 to 800 nm is 91.5%, the transmittance at a wavelength of 1100 nm is8.3%, the IR cut-off wavelength is 837 nm, and the UV cut-off wavelengthis 391 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed onthe infrared-absorbing layer ira12. A coating liquid UVA1 as used inExample 1 was applied onto the protective layer p2 by spin coating andthe resultant film was cured by heating at 140° C. for 30 minutes toform an ultraviolet-absorbing layer uva1. The thickness of theultraviolet-absorbing layer uva1 is 6 μm. An anti-reflection film ar2was formed on the ultraviolet-absorbing layer uva1 using a vacuumdeposition apparatus. The anti-reflection film ar2 is a film composed ofSiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and hasa total thickness of about 0.4 μm. An optical filter according toExample 4 was thus obtained.

Transmittance spectra of the optical filter according to Example 4 areshown in FIG. 13B and Table 22. The optical filter according to Example4 has the characteristics shown in Table 23. In the same manner as inExample 1, the normalized spectral sensitivity functions CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ) were determined based on the spectraltransmittance T_(θ)(λ) shown by the optical filter according to Example4 for light incident at incident angles θ of 0°, 30°, and 40° and R(λ),G(λ), and B(λ) shown in Table (I). FIG. 14A, FIG. 14B, and FIG. 14C showthe normalized spectral sensitivity functions at incident angle θ of 0°,30°, and 40°. FIG. 15A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functions at anincident angle θ of 30° from the normalized spectral sensitivityfunction at an incident angle θ of 0°. FIG. 15B is a graph showingdifferences obtained by subtracting each of the normalized spectralsensitivity functions at an incident angle θ of 40° from the normalizedspectral sensitivity function at an incident angle θ of 0°. FIG. 15C isa graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 40°from the normalized spectral sensitivity function at an incident angle θof 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB);IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); andISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) weredetermined by the above equations (1) to (9) using the normalizedspectral sensitivity functions determined for two incident angles θ1°and θ2° (θ1<θ2) selected from 0°, 30°, and 40°. Tables 24 to 26 show theresults.

Example 5

A coating liquid IRA1 was prepared in the same manner as in Example 1.The coating liquid IRA1 was applied to one principal surface of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) using a die coater. The resultant film was cured by heattreatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. The totalthickness of the infrared-absorbing layer ira11 and infrared-absorbinglayer ira12 is 0.2 mm.

Next, an infrared-reflecting film irr1 was formed on theinfrared-absorbing layer ira11 using a vacuum deposition apparatus inthe same manner as in Example 4. The infrared-reflecting film irr1 iscomposed of SiO₂ and TiO₂ that are alternately laminated in 16 layers.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed onthe infrared-absorbing layer ira12. A coating liquid UVRA1 as used inExample 2 was applied onto the protective layer p2 under the sameconditions as in Example 2 and the resultant film was cured by heatingat 140° C. for 30 minutes to form an infrared- and ultraviolet-absorbinglayer uvira1. The thickness of the infrared- and ultraviolet-absorbinglayer uvira1 is 7 μm. An anti-reflection film ar2 was formed on theinfrared- and ultraviolet-absorbing layer uvira1 using a vacuumdeposition apparatus. The anti-reflection film ar2 is a film composed ofSiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and hasa total thickness of about 0.4 μm. An optical filter according toExample 5 was thus obtained.

Transmittance spectra of the optical filter according to Example 5 areshown in FIG. 16 and Table 27. The optical filter according to Example 5has the characteristics shown in Table 28. In the same manner as inExample 1, the normalized spectral sensitivity functions CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ) were determined based on the spectraltransmittance T_(θ)(λ) shown by the optical filter according to Example5 for light incident at incident angles θ of 0°, 30°, and 40° and R(λ),G(λ), and B(λ) shown in Table (I). FIG. 17A, FIG. 17B, and FIG. 17C showthe normalized spectral sensitivity functions at incident angle θ of 0°,30°, and 40°. FIG. 18A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functions at anincident angle θ of 30° from the normalized spectral sensitivityfunction at an incident angle θ of 0°. FIG. 18B is a graph showingdifferences obtained by subtracting each of the normalized spectralsensitivity functions at an incident angle θ of 40° from the normalizedspectral sensitivity function at an incident angle θ of 0°. FIG. 18C isa graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 40°from the normalized spectral sensitivity function at an incident angle θof 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB);IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); andISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) weredetermined by the above equations (1) to (9) using the normalizedspectral sensitivity functions determined for two incident angles θ1°and θ2° (θ1<θ2) selected from 0°, 30°, and 40°. Tables 29 to 31 show theresults.

Example 6

Coating liquids IRA1 and IRA2 were prepared in the same manner as inExample 1. The coating liquid IRA1 was applied to one principal surfaceof a transparent glass substrate (manufactured by SCHOTT AG, productname: D 263 T eco) using a die coater. The resultant film was cured byheat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours,at 150° C. for 1 hour, and then at 170° C. for 3 hours to form aninfrared-absorbing layer ira11. In the same manner, the coating liquidIRA1 was applied to the other principal surface of the transparent glasssubstrate. The resultant film was cured by heat treatment under the sameconditions as above to form an infrared-absorbing layer ira12. The totalthickness of the infrared-absorbing layer ira11 and infrared-absorbinglayer ira12 is 0.4 mm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed onthe infrared-absorbing layer ira11 using a vacuum deposition apparatus.In the same manner, a 500-nm-thick SiO₂-deposited film (protective layerp2) was formed on the infrared-absorbing layer ira12. The coating liquidIRA2 was applied to the surface of the protective layer p1 with a diecoater. The resultant film was cured by heat treatment in an oven at 85°C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and thenat 170° C. for 3 hours to form an infrared-absorbing layer ira21. Thecoating liquid IRA2 was applied also to the surface of the protectivelayer p2 with a die coater. The resultant film was cured under the sameheating conditions to form an infrared-absorbing layer ira22. Anintermediate product δ was thus obtained. A transmittance spectrum shownby the intermediate product δ at an incident angle of 0° C. is shown inFIG. 19A. The intermediate product δ has the following characteristics(δ1) to (δ8).

(δ1): The average transmittance in the wavelength range of 700 to 1100nm is 0.5% or less.

(δ2): The average transmittance in the wavelength range of 700 to 1000nm is 0.5% or less.

(δ3): The average transmittance in the wavelength range of 1100 to 1200nm is 0.5% or less.

(δ4): The average transmittance in the wavelength range of 450 to 600 nmis 82.2%.

(δ5): The average transmittance in the wavelength range of 500 to 600 nmis 82.7%.

(δ6): The transmittance at a wavelength of 400 nm is 42.0% and thetransmittance at a wavelength of 450 nm is 76.7%.

(δ7): The IR cut-off wavelength is 613 nm, the UV cut-off wavelength is404 nm, and the full width at half maximum of the transmission region is209 nm.

(δ8): The wavelength which lies in the wavelength range of 600 to 800 nmand at which the spectral transmittance is 20% is 637 nm.

An anti-reflection film ar1 was formed on the infrared-absorbing layerira21 using a vacuum deposition apparatus. An anti-reflection film ar2was formed on the infrared-absorbing layer ira22 using a vacuumdeposition apparatus. The specifications of the anti-reflection film ar1and anti-reflection film ar2 are the same. Each of the anti-reflectionfilm ar1 and anti-reflection film ar2 is a film composed of SiO₂ andTiO₂ that are alternately laminated, includes 7 layers, and has a totalthickness of about 0.4 μm. An optical filter according to Example 6 wasthus obtained.

Transmittance spectra of the optical filter according to Example 6 areshown in FIG. 19B and Table 32. The optical filter according to Example6 has the characteristics shown in Table 33. In the same manner as inExample 1, the normalized spectral sensitivity functions CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ) were determined based on the spectraltransmittance Tθ(λ) shown by the optical filter according to Example 6for light incident at incident angles θ of 0°, 30°, and 40° and R(λ),G(λ), and B(λ) shown in Table (I). FIG. 20A, FIG. 20B, and FIG. 20C showthe normalized spectral sensitivity functions at incident angle θ of 0°,30°, and 40°. FIG. 21A is a graph showing differences obtained bysubtracting each of the normalized spectral sensitivity functions at anincident angle θ of 30° from the normalized spectral sensitivityfunction at an incident angle θ of 0°. FIG. 21B is a graph showingdifferences obtained by subtracting each of the normalized spectralsensitivity functions at an incident angle θ of 40° from the normalizedspectral sensitivity function at an incident angle θ of 0°. FIG. 21C isa graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 40°from the normalized spectral sensitivity function at an incident angle θof 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB);IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB); andISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) weredetermined by the above equations (1) to (9) using the normalizedspectral sensitivity functions determined for two incident angles θ1°and θ2° (θ1<θ2) selected from 0°, 30°, and 40°. Tables 34 to 36 show theresults.

Comparative Example 1

An infrared-reflecting film irr2 was formed on one principal surface ofa transparent glass substrate (manufactured by SCHOTT AG, product name:D 263 T eco) by alternately laminating SiO₂ and TiO₂ in 24 layers usinga vacuum deposition apparatus. An intermediate product ε was thusobtained. Transmittance spectra of the intermediate product ε are shownin FIG. 22A. The intermediate product ε has the followingcharacteristics (ε1) to (ε3).

(ε1): When the incident angle of light is 0°, the transmittance at awavelength of 380 nm is 0.5% or less, the transmittance at a wavelengthof 400 nm is 3.1%, the average transmittance in the wavelength range of450 to 600 nm is 94.1%, the lowest transmittance in the wavelength rangeof 450 to 600 nm is 92.6%, the transmittance at a wavelength of 700 nmis 86.2%, the transmittance at a wavelength of 715 nm is 30.8%, theaverage transmittance in the wavelength range of 700 to 800 nm is 12.4%,the transmittance at a wavelength of 1100 nm is 0.5% or less, the IRcut-off wavelength is 710 nm, and the UV cut-off wavelength is 410 nm.

(ε2): When the incident angle of light is 30°, the transmittance at awavelength of 380 nm is 1.7%, the transmittance at a wavelength of 400nm is 77.7%, the average transmittance in the wavelength range of 450 to600 nm is 94.1%, the lowest transmittance in the wavelength range of 450to 600 nm is 93.0%, the transmittance at a wavelength of 700 nm is 8.2%,the transmittance at a wavelength of 715 nm is 2.2%, the averagetransmittance in the wavelength range of 700 to 800 nm is 1.1%, thetransmittance at a wavelength of 1100 nm is 1.2%, the IR cut-offwavelength is 680 nm, and the UV cut-off wavelength is 397 nm.

(ε3): When the incident angle of light is 40°, the transmittance at awavelength of 380 nm is 13.1%, the transmittance at a wavelength of 400nm is 90.5%, the average transmittance in the wavelength range of 450 to600 nm is 92.1%, the lowest transmittance in the wavelength range of 450to 600 nm is 87.6%, the transmittance at a wavelength of 700 nm is 2.0%,the transmittance at a wavelength of 715 nm is 0.8%, the averagetransmittance in the wavelength range of 700 to 800 nm is 0.5% or less,the transmittance at a wavelength of 1100 nm is 5.4%, the IR cut-offwavelength is 661 nm, and the UV cut-off wavelength is 386 nm.

A coating liquid IRA3 containing an infrared-absorbing dye was preparedin the following manner. The infrared-absorbing dye is a combination ofa cyanine-based organic dye and squarylium-based organic dye and issoluble in MEK. The infrared-absorbing dye was added to MEK serving as asolvent, and PVB serving as a matrix was also added thereto, followed bystirring for 2 hours to obtain the coating liquid IRA3. The content ofthe matrix in the solids of the coating liquid IRA3 was 99 mass %. Thecoating liquid IRA3 was applied onto the other principal surface of thetransparent glass substrate of the intermediate product ε by spincoating, and the resultant film was cured by heating at 140° C. for 30minutes to form an infrared-absorbing layer ira3. Separately, aninfrared-absorbing layer was formed on one principal surface of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) under the same conditions as those for the formation of theinfrared-absorbing layer ira3 to produce a laminate according toReference Example 5. A transmittance spectrum shown by the laminateaccording to Reference Example 5 at an incident angle of 0° is shown inFIG. 22B. The laminate according to Reference Example 5 has thefollowing characteristics (v1) to (v4).

-   -   (v1): The transmittance at a wavelength of 700 nm is 2.0%, the        transmittance at a wavelength of 715 nm is 2.6%, and the average        transmittance in the wavelength range of 700 to 800 nm is 15.9%.

(v2): The transmittance at a wavelength of 1100 nm is 91.1%.

(v3): The transmittance at a wavelength of 400 nm is 78.2%, thetransmittance at a wavelength of 450 nm is 83.8%, and the averagetransmittance in the wavelength range of 500 to 600 nm is 86.9%.

(v4): The IR cut-off wavelength in the wavelength range of 600 nm to 700nm is 637 nm, the IR cut-off wavelength in the wavelength range of 700nm to 800 nm is 800 nm, the difference between these IR cut-offwavelengths is 163 nm, and the wavelength of maximum absorption in thewavelength range of 600 nm to 800 nm is 706 nm.

An anti-reflection film ar1 was formed on the infrared-absorbing layerira3 using a vacuum deposition apparatus in the same manner as inExample 1 to obtain an optical filter according to Comparative Example1.

Transmittance spectra of the optical filter according to ComparativeExample 1 are shown in FIG. 22C and Table 37. The optical filteraccording to Comparative Example 1 has the characteristics shown inTable 38. In the same manner as in Example 1, the normalized spectralsensitivity functions CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) weredetermined based on the spectral transmittance T_(θ)(λ) shown by theoptical filter according to Comparative Example 1 for light incident atincident angles θ of 0°, 30°, and 40 and R(λ), G(λ), and B(λ) shown inTable (I). FIG. 23A, FIG. 23B, and FIG. 23C show the normalized spectralsensitivity functions at incident angle θ of 0°, 30°, and 40°. FIG. 24Ais a graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 30°from the normalized spectral sensitivity function at an incident angle θof 0°. FIG. 24B is a graph showing differences obtained by subtractingeach of the normalized spectral sensitivity functions at an incidentangle θ of 40° from the normalized spectral sensitivity function at anincident angle θ of 0°. FIG. 24C is a graph showing differences obtainedby subtracting each of the normalized spectral sensitivity functions atan incident angle θ of 40° from the normalized spectral sensitivityfunction at an incident angle θ of 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2)^(CG), and IE_(θ1/θ2) ^(CB); IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), andIAE_(θ1/θ2) ^(CB); and ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), andISE_(θ1/θ2) ^(CB) were determined by the above equations (1) to (9)using the normalized spectral sensitivity functions determined for twoincident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40°.Tables 39 to 41 show the results.

Comparative Example 2

An infrared-absorbing glass substrate showing the transmittance spectrumshown in FIG. 25A at an incident angle of 0° was prepared. Theinfrared-absorbing glass substrate has the following characteristics(g1) to (g5).

(g1): The average transmittance in the wavelength range of 700 to 1000nm is 16.8%.

(g2): The average transmittance in the wavelength range of 1100 to 1200nm is 38.5%.

(g3): The average transmittance in the wavelength range of 450 to 600 nmis 87.8%.

(g4): The transmittance at a wavelength of 400 nm is 88.5%.

(g5): The IR cut-off wavelength is 653 nm. The wavelength which lies inthe wavelength range of 600 to 800 nm and at which the transmittance is20% is 738 nm.

An infrared-reflecting film irr3 was formed on one principal surface ofthe infrared-absorbing glass substrate, which has a thickness of 210 μm,by alternately laminating SiO₂ and TiO₂ in 20 layers using a vacuumdeposition apparatus. An intermediate product was thus obtained. Aninfrared-reflecting film was formed on one principal surface of atransparent glass substrate (manufactured by SCHOTT AG, product name: D263 T eco) under the same conditions as for the formation of theinfrared-reflecting film irr3 to obtain a laminate according toReference Example 6. Transmittance spectra of the laminate according toReference Example 6 are shown in FIG. 25B. The laminate according toReference Example 6 has the following characteristics (w1) to (w3).

(w1): When the incident angle of light is 0°, the transmittance at awavelength of 380 nm is 0.5% or less, the transmittance at a wavelengthof 400 nm is 0.5% or less, the average transmittance in the wavelengthrange of 450 to 600 nm is 95.2%, the lowest transmittance in thewavelength range of 450 to 600 nm is 93.7%, the average transmittance inthe wavelength range of 700 to 800 nm is 4.7%, the transmittance at awavelength of 1100 nm is 0.5% or less, the IR cut-off wavelength is 702nm, and the UV cut-off wavelength is 411 nm.

(w2): When the incident angle of light is 30°, the transmittance at awavelength of 380 nm is 1.7%, the transmittance at a wavelength of 400nm is 77.7%, the average transmittance in the wavelength range of 450 to600 nm is 94.1%, the lowest transmittance in the wavelength range of 450to 600 nm is 93.0%, the average transmittance in the wavelength range of700 to 800 nm is 1.1%, the transmittance at a wavelength of 1100 nm is1.2%, the IR cut-off wavelength is 680 nm, and the UV cut-off wavelengthis 397 nm.

(w3): When the incident angle of light is 40°, the transmittance at awavelength of 380 nm is 13.1%, the transmittance at a wavelength of 400nm is 90.5%, the average transmittance in the wavelength range of 450 to600 nm is 92.1%, the lowest transmittance in the wavelength range of 450to 600 nm is 87.6%, the average transmittance in the wavelength range of700 to 800 nm is 0.5% or less, the transmittance at a wavelength of 1100nm is 5.4%, the IR cut-off wavelength is 661 nm, and the UV cut-offwavelength is 386 nm.

A coating liquid UVIRA2 containing an infrared-absorbing dye andultraviolet-absorbing dye was prepared in the following manner. Theultraviolet-absorbing dye is a dye composed of a benzophenone-basedultraviolet-absorbing substance which is less likely to absorb light inthe visible region. The infrared-absorbing dye is a combination of acyanine-based organic dye and squarylium-based organic dye. Theinfrared-absorbing dye and ultraviolet-absorbing dye are soluble in MEK.The infrared-absorbing dye and ultraviolet-absorbing dye were added toMEK serving as a solvent, and PVB serving as a matrix was also addedthereto, followed by stirring for 2 hours to obtain a coating liquidUVIRA2. The content of PVB in the solids of the coating liquid UVIRA2was 60 mass %. The coating liquid UVIRA2 was applied onto the otherprincipal surface of the intermediate product ζ, and the resultant filmwas cured by heating to form an infrared- and ultraviolet-absorbinglayer uvira2. The thickness of the infrared- and ultraviolet-absorbinglayer uvira2 is 7 μm. An infrared- and ultraviolet-absorbing layer wasformed on one principal surface of a transparent glass substrate(manufactured by SCHOTT AG, product name: D 263 T eco) using the coatingliquid UVIRA2 under the same conditions as those for the formation ofthe infrared- and ultraviolet-absorbing layer uvira2 to produce alaminate according to Reference Example 7. A transmittance spectrumshown by the laminate according to Reference Example 7 at an incidentangle of 0° is shown in FIG. 25C. The laminate according to ReferenceExample 7 has the following characteristics (p1) to (p5).

(p1): The transmittance at a wavelength of 700 nm is 4.9%, thetransmittance at a wavelength of 715 nm is 8.4%, and the averagetransmittance in the wavelength range of 700 to 800 nm is 63.9%.

(p2): The transmittance at a wavelength of 1100 nm is 92.3%.

(p3): The transmittance at a wavelength of 400 nm is 12.6%, thetransmittance at a wavelength of 450 nm is 84.4%, and the averagetransmittance in the wavelength range of 500 to 600 nm is 88.7%.

(p4): The IR cut-off wavelength in the wavelength range of 600 nm to 700nm is 664 nm, the IR cut-off wavelength in the wavelength range of 700nm to 800 nm is 731 nm, and the difference therebetween is 67 nm. Thewavelength (wavelength of maximum absorption) at which the transmittanceis the lowest in the wavelength range of 600 nm to 800 nm is 705 nm.

(p5): The UV cut-off wavelength in the wavelength range of 350 nm to 450nm is 411 nm.

In the same manner as in Example 1, an anti-reflection film ar1 wasformed on the infrared- and ultraviolet-absorbing layer uvira2 using avacuum deposition apparatus. The anti-reflection film ar1 is a filmcomposed of SiO₂ and TiO₂ that are alternately laminated, includes 7layers, and has a total thickness of about 0.4 μm. An optical filteraccording to Comparative Example 2 was thus obtained.

Transmittance spectra of the optical filter according to ComparativeExample 2 are shown in FIG. 25D and Table 42. The optical filteraccording to Comparative Example 2 has the characteristics shown inTable 43. In the same manner as in Example 1, the normalized spectralsensitivity functions CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) weredetermined based on the spectral transmittance T_(θ)(λ) shown by theoptical filter according to Comparative Example 2 for light incident atincident angles θ of 0°, 30°, and 40 and R(λ), G(λ), and B(λ) shown inTable (I). FIG. 26A, FIG. 26B, and FIG. 26C show the normalized spectralsensitivity functions at incident angle θ of 0°, 30°, and 40°. FIG. 27Ais a graph showing differences obtained by subtracting each of thenormalized spectral sensitivity functions at an incident angle θ of 30°from the normalized spectral sensitivity function at an incident angle θof 0°. FIG. 27B is a graph showing differences obtained by subtractingeach of the normalized spectral sensitivity functions at an incidentangle θ of 40° from the normalized spectral sensitivity function at anincident angle θ of 0°. FIG. 27C is a graph showing differences obtainedby subtracting each of the normalized spectral sensitivity functions atan incident angle θ of 40° from the normalized spectral sensitivityfunction at an incident angle θ of 30°. IE_(θ1/θ2) ^(CR), IE_(θ1/θ2)^(CG), and IE_(θ1/θ2) ^(CB); IAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), andIAE_(θ1/θ2) ^(CB); and ISE_(θ1/θ2) ^(CR), ISE_(θ1/θ2) ^(CG), andISE_(θ1/θ2) ^(CB) were determined by the above equations (1) to (9)using the normalized spectral sensitivity functions determined for twoincident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40°.Tables 44 to 46 show the results.

The requirements (i) to (vii) are satisfied by the optical filtersaccording to Examples 1 to 6. The optical filters according to Examples1 to 6 have sufficiently low transmittances in the wavelength range of700 nm or more, which indicates that the optical filters according toExamples 1 to 6 can shield against near-infrared light well. In thewavelength range of 700 nm or more, the optical filter according toExample 2 exhibits lower transmittances than those of the optical filteraccording to Example 1. Since the optical filter according to Example 2includes the organic infrared-absorbing dye, the transmittances of theoptical filter according to Example 2 are lower in the visible regionthan those of the optical filter according to Example 1 by about 2points. This is nevertheless not considered a practical issue. Theoptical filter according to Example 3, which includes only theinfrared-absorbing layer ira11 and infrared-absorbing layer ira12 asinfrared-absorbing layers, exhibits higher transmittances in thewavelength range of 1100 nm or more than in the wavelength range of 700to 1100 nm and than the transmittances of the optical filters accordingto Examples 1 and 2 in the wavelength range of 1100 nm or more.Nevertheless, the optical filter according to Example 3 is considered tohave appropriate characteristics for imaging apparatuses because imagingdevices such as CMOS sensors have a low sensitivity to light with awavelength of 1100 nm or more. Although higher than the transmittancesof the optical filters of other Examples at around a wavelength of 400nm, the transmittance of the optical filter according to Example 6 ataround a wavelength of 400 nm is 45% or less.

The requirements shown in Tables (II) to (IV) are satisfied by theoptical filters according to Examples 1 to 6. Additionally, the spectraltransmittances shown by each of the optical filters according toExamples 1 to 6 at incident angles of 0°, 30°, and 40° are almost thesame. This indicates that when each of the optical filters according toExamples 1 to 6 is incorporated in an imaging apparatus, a variation inincident angle of light incident on the optical filter causes only asmall change in a sensitivity curve drawn based on output from theimaging apparatus. The infrared-reflecting films of the optical filtersaccording to Examples 4 and 5 are configured so that the boundarybetween a wavelength band of light that is incident at an incident angleof 400 and is transmitted and a wavelength band of light that isincident at an incident angle of 40° and is reflected is around 850 nm.Thus, the spectral transmittances shown by each of the optical filtersaccording to Examples 4 and 5 at incident angles of 0°, 30°, and 40° arealmost the same. The larger the incident angle of light incident on theoptical filters according to Examples 4 and 5 is, the highertransmittances the optical filters according to Examples 4 and 5 exhibitaround a wavelength of 400 nm. This affects the values of IE_(θ1/θ2)^(CB), IAE_(θ1/θ2) ^(CB), and ISE_(θ1/θ2) ^(CB) when θ1=0 and θ2=30 andwhen θ1=0 and θ2=40. Additionally, around a wavelength of 530 nm, thetransmittances shown by the optical filters according to Examples 4 and5 at an incident angle of 30° are higher than the transmittances shownthereby at incident angles of 0° and 40°. This affects the values ofIE_(θ1/θ2) ^(CG), IAE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CG) when θ1=0 andθ2=30 and when θ1=30 and θ2=40. However, these effects are so small thatthe requirements shown in Tables (II) to (IV) are satisfied. Therefore,it is thought that when each of the optical filters according toExamples 1 to 6 is incorporated in an imaging apparatus such as a cameramodule, incidence of light on the optical filter at an incident angle inthe range of 0° to 40° does not cause uneven coloring of a taken image.

In a part of the visible light region and adjacent to the near-infraredregion and the near-infrared region, the infrared-absorbing layer ira3of the optical filter according to Comparative Example 1 determines theboundary between a light transmission wavelength band and a lightshielding wavelength band. However, because of a narrow absorption bandof the infrared-absorbing layer ira3, the transmittance spectrum of theoptical filter according to Comparative Example 1 is affected moregreatly by the effect of a shift of a reflection band of theinfrared-reflecting film to the short wavelength side as the incidentangle of light increases. Moreover, the optical filter according toComparative Example 1, which has an insufficient ability to absorb lightin the ultraviolet region, substantially uses the infrared-reflectingfilm irr2 alone to shield against light in the ultraviolet region. Thus,in the ultraviolet region, the optical filter according to ComparativeExample 1 is strongly affected by the effect of the incidentangle-dependent shift of the reflection band to the short wavelengthside. For the optical filter according to Comparative Example 1,CB_(θ)(λ) at an incident angle of 0° and that at an incident angle of30° greatly differ around 400 nm. Moreover, for the optical filteraccording to Comparative Example 1, CR_(θ)(λ) at an incident angle of30° and that at an incident angle of 40° greatly differ around 650 nm.For the optical filter according to Comparative Example 1, CB_(θ)(λ) atan incident angle of 0° and that at an incident angle of 30° differ, andCB_(θ)(A) at an incident angle of 30 and that at an incident angle of40° also differ in a narrow wavelength band. Thus, the value ofIE_(θ1/θ2) ^(CB) is large when θ1=30 and θ2=40. Additionally, the valuesof IE_(θ1/θ2), IAE_(θ1/θ2), and ISE_(θ1/θ2) are large when θ1=30 andθ2=40. Therefore, there is concern that when this optical filter isincorporated in an imaging apparatus, a narrow area of an image obtainedusing the imaging apparatus may be colored quite unevenly.

In a part of the visible light region adjacent to the near-infraredregion and the near-infrared region, and the ultraviolet region, theinfrared- and ultraviolet-absorbing layer uvira2 of the optical filteraccording to Comparative Example 2 determines the boundary between alight transmission wavelength band and a light shielding wavelengthband. However, because of a narrow absorption band of the infrared- andultraviolet-absorbing layer uvira2 in the near-infrared region, areflection band determined by the infrared-reflecting film irr3 of theoptical filter according to Comparative Example 2 cannot be set on asufficiently long wavelength side. Therefore, the optical filteraccording to Comparative Example 2 is more inevitably affected by theeffect of a shift of the reflection band to the short wavelength side asthe incident angle of light increases. IE_(θ1/θ2), IAE_(θ1/θ2), andISE_(θ1/θ2) are within the value ranges shown in Table (II) when θ1=0and θ2=30. However, a local variation (ripple) in transmittance isobserved in the visible region of the transmittance spectrum shown bythe optical filter according to Comparative Example 2 at an incidentangle of 40°. Thus, IE_(θ1/θ2), IAE_(θ1/θ2), and ISE_(θ1/θ2) are largewhen θ1=30 and θ2=40. There is concern that when this optical filter isincorporated in an imaging apparatus, a narrow area of an image obtainedusing the imaging apparatus may be colored quite unevenly.

TABLE 7 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.1 0.1 0.1 400 9.3 8.2 7.3 410 44.6 42.8 41.1 420 70.4 69.6 68.3430 80.4 80.4 79.5 440 84.3 84.7 83.9 450 87.1 87.7 87.0 460 88.9 89.588.7 470 89.7 90.2 89.3 480 91.1 91.5 90.6 490 92.9 93.3 92.2 500 92.492.6 91.4 510 93.9 94.1 92.8 520 93.6 93.6 92.3 530 94.1 94.2 92.8 54093.5 93.4 92.0 550 94.0 93.9 92.6 560 92.3 92.1 90.7 570 92.1 91.9 90.5580 88.8 88.4 87.0 590 86.1 85.6 84.2 600 80.6 79.8 78.4 610 73.0 71.970.4 620 64.5 63.2 61.6 630 53.4 51.8 50.0 640 41.5 39.7 38.0 650 30.228.4 26.8 660 20.0 18.4 17.0 670 12.3 11.0 9.9 680 7.0 6.0 5.3 690 3.83.2 2.7 700 1.9 1.5 1.3 710 1.0 0.7 0.6 715 0.7 0.5 0.4 730 0.3 0.2 0.1740 0.1 0.1 0.1 750 0.1 0.1 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.00.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.00.0 0.0 960 0.0 0.0 0.0 980 0.1 0.0 0.0 1000 0.1 0.1 0.0 1020 0.1 0.10.1 1040 0.2 0.1 0.1 1060 0.3 0.2 0.2 1080 0.5 0.4 0.3 1100 0.9 0.6 0.51120 1.4 1.0 0.8 1140 2.1 1.6 1.3 1160 3.2 2.6 2.2 1180 4.7 3.9 3.3 12006.6 5.6 4.9

TABLE 8 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength IR cut-off UV cut-off maximum inIncident range of 700 to range of 700 to range of 1100 range of 500 towavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] to1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less3.0 91.5 633 412 221 30° 0.5 or less 0.5 or less 2.4 91.4 631 412 21940° 0.5 or less 0.5 or less 2.1 90.0 630 413 217

TABLE 9 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.29 0.310.04 1.26 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 2.902.01 1.16 1.74 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range1.61 1.70 1.12 0.58

TABLE 10 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.320.55 0.60 0.77 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.90 2.01 1.16 1.74 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.61 1.70 1.12 0.58

TABLE 11 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.010.001 0.003 0.01 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.07 0.02 0.01 0.06 ISE_(30/40) ^(CR) ISE_(30/40) ^(CG)ISE_(30/40) ^(CB) Range 0.02 0.02 0.01 0.01

TABLE 12 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.1 0.1 0.1 400 8.3 7.3 6.5 410 40.0 38.2 36.5 420 63.5 62.5 61.0430 74.2 73.9 72.8 440 78.9 78.9 78.0 450 82.2 82.5 81.5 460 85.6 86.085.1 470 87.8 88.2 87.2 480 89.7 90.0 89.0 490 91.7 92.0 90.9 500 91.491.5 90.3 510 92.9 93.0 91.7 520 92.4 92.4 91.1 530 93.1 93.1 91.7 54092.4 92.2 90.8 550 92.5 92.3 90.9 560 90.3 90.0 88.6 570 89.7 89.3 87.9580 85.6 85.0 83.6 590 81.6 80.9 79.4 600 74.5 73.5 72.0 610 65.3 63.962.2 620 54.7 53.1 51.3 630 41.9 40.1 38.3 640 30.0 28.1 26.5 650 20.218.5 17.1 660 11.8 10.5 9.5 670 5.8 4.9 4.3 680 2.1 1.7 1.4 690 0.6 0.40.3 700 0.1 0.1 0.1 710 0.1 0.0 0.0 715 0.1 0.0 0.0 730 0.1 0.1 0.0 7400.1 0.0 0.0 750 0.0 0.0 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.00.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 8600.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.00.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.1 0.01040 0.1 0.1 0.1 1060 0.2 0.1 0.1 1080 0.3 0.2 0.2 1100 0.6 0.4 0.3 11200.9 0.7 0.6 1140 1.5 1.1 0.9 1160 2.3 1.8 1.5 1180 3.5 2.9 2.5 1200 5.24.3 3.7

TABLE 13 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 2.2 89.4 624 413 210 30° 0.5 or less 0.5 or less 1.8 89.0 622 414208 40° 0.5 or less 0.5 or less 1.5 87.7 621 415 206

TABLE 14 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.28 0.410.19 1.09 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 2.802.16 1.39 1.41 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range1.51 1.75 1.20 0.55

TABLE 15 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.300.57 0.53 0.77 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.80 2.16 1.39 1.41 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.51 1.75 1.20 0.55

TABLE 16 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.020.002 0.003 0.02 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.07 0.03 0.01 0.06 ISE_(30/40) ^(CR) ISE_(30/40) ^(CG)ISE_(30/40) ^(CB) Range 0.02 0.02 0.01 0.01

TABLE 17 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.1 0.1 0.1 400 9.1 8.0 7.2 410 44.6 42.8 41.1 420 70.8 70.0 68.7430 81.1 81.2 80.3 440 85.1 85.6 84.8 450 88.1 88.7 88.0 460 89.9 90.689.8 470 90.8 91.3 90.5 480 92.2 92.7 91.7 490 93.9 94.3 93.3 500 93.393.6 92.4 510 94.8 95.0 93.8 520 94.4 94.5 93.3 530 94.9 95.0 93.7 54094.1 94.1 92.7 550 94.6 94.5 93.2 560 92.8 92.6 91.2 570 92.4 92.2 90.9580 89.0 88.6 87.3 590 86.0 85.5 84.1 600 80.1 79.4 77.9 610 72.0 71.069.4 620 63.1 61.7 60.0 630 51.4 49.8 48.0 640 39.3 37.4 35.7 650 27.926.1 24.5 660 18.0 16.4 15.1 670 10.7 9.4 8.5 680 5.9 5.0 4.4 690 3.12.5 2.2 700 1.5 1.2 1.0 710 0.8 0.6 0.5 715 0.5 0.4 0.3 730 0.2 0.1 0.1740 0.1 0.1 0.1 750 0.1 0.0 0.0 760 0.1 0.0 0.0 770 0.0 0.0 0.0 780 0.00.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.1 0.0 0.0 940 0.10.1 0.1 960 0.2 0.2 0.1 980 0.4 0.3 0.2 1000 0.6 0.4 0.3 1020 0.9 0.70.5 1040 1.4 1.1 0.9 1060 2.4 1.9 1.5 1080 4.1 3.3 2.8 1100 6.7 5.6 4.81120 10.2 8.8 7.8 1140 14.6 12.8 11.6 1160 19.8 17.8 16.3 1180 24.9 22.821.2 1200 30.0 27.9 26.2

TABLE 18 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 17.5 92.0 631 412 219 30° 0.5 or less 0.5 or less 15.8 91.9 630 412218 40° 0.5 or less 0.5 or less 14.4 90.5 629 413 216

TABLE 19 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.26 0.26−0.01   1.28 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 2.831.92 1.07 1.76 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range1.57 1.66 1.09 0.57

TABLE 20 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.290.56 0.63 0.73 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.83 1.92 1.07 1.76 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.57 1.66 1.09 0.57

TABLE 21 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.010.001 0.003 0.01 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.07 0.02 0.01 0.06 ISE_(30/40) ^(CR) ISE_(30/40) ^(CG)ISE_(30/40) ^(CB) Range 0.02 0.02 0.01 0.01

TABLE 22 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.0 0.0 0.0 400 0.7 5.8 7.0 410 23.0 41.7 40.0 420 69.6 68.7 69.4430 78.5 82.4 80.6 440 84.8 86.4 85.2 450 88.9 89.2 88.8 460 89.7 91.490.3 470 90.2 92.0 91.0 480 91.6 93.3 92.5 490 93.5 95.3 93.6 500 93.194.7 91.8 510 94.4 96.0 92.9 520 93.3 95.7 92.8 530 93.1 96.3 93.9 54092.4 95.5 93.6 550 93.3 95.8 94.6 560 92.0 94.0 92.8 570 91.9 93.8 92.3580 89.0 90.4 88.3 590 86.5 87.0 84.7 600 81.1 80.6 78.6 610 73.2 71.970.5 620 64.1 62.8 61.6 630 52.3 51.3 49.9 640 40.2 39.2 37.4 650 29.027.8 25.9 660 19.0 17.7 16.1 670 11.6 10.4 9.2 680 6.6 5.6 4.9 690 3.52.9 2.5 700 1.8 1.4 1.2 710 0.9 0.7 0.6 715 0.6 0.5 0.4 730 0.3 0.2 0.1740 0.2 0.1 0.1 750 0.1 0.1 0.0 760 0.1 0.0 0.0 770 0.0 0.0 0.0 780 0.00.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.00.0 0.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.00.0 1040 0.1 0.1 0.1 1060 0.1 0.1 0.1 1080 0.2 0.2 0.3 1100 0.4 0.4 0.61120 0.6 0.8 1.2 1140 1.0 1.4 2.3 1160 1.5 2.4 4.2 1180 2.3 4.0 7.4 12003.3 6.6 12.4

TABLE 23 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 1.4 91.3 632 414 218 30° 0.5 or less 0.5 or less 2.4 93.3 631 413218 40° 0.5 or less 0.5 or less 4.2 91.1 630 413 217

TABLE 24 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 0.43 −2.2−2.67 3.09 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 2.240.32 −1.29 3.53 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range1.81 2.51 1.38 1.13

TABLE 25 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.562.70 2.91 1.35 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.77 1.73 2.07 1.03 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.83 2.53 1.50 1.03

TABLE 26 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.010.05 0.13 0.12 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range0.06 0.02 0.1 0.09 ISE_(30/40) ^(CR) ISE_(30/40) ^(CG) ISE_(30/40) ^(CB)Range 0.03 0.05 0.01 0.03

TABLE 27 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.0 0.0 0.0 400 0.7 5.4 6.4 410 21.0 37.9 36.3 420 63.7 62.6 62.9430 73.3 76.6 74.6 440 80.1 81.2 79.9 450 84.5 84.6 84.0 460 87.1 88.587.3 470 88.9 90.5 89.4 480 90.7 92.3 91.4 490 92.6 94.4 92.7 500 92.594.0 91.2 510 93.7 95.2 92.1 520 92.4 94.8 91.8 530 92.4 95.5 93.0 54091.5 94.6 92.7 550 92.0 94.4 93.1 560 90.3 92.2 91.0 570 89.9 91.7 90.1580 86.3 87.5 85.3 590 82.8 83.2 80.8 600 76.2 75.4 73.3 610 67.0 65.563.9 620 56.2 54.7 53.3 630 43.1 41.7 40.3 640 31.0 29.8 28.1 650 21.220.0 18.4 660 12.8 11.6 10.4 670 6.4 5.5 4.8 680 2.5 2.0 1.7 690 0.7 0.50.4 700 0.2 0.1 0.1 710 0.1 0.1 0.0 715 0.1 0.1 0.1 730 0.2 0.1 0.1 7400.1 0.1 0.1 750 0.1 0.1 0.0 760 0.1 0.0 0.0 770 0.1 0.0 0.0 780 0.0 0.00.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 8600.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.00.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.0 0.01040 0.1 0.1 0.1 1060 0.1 0.1 0.1 1080 0.2 0.2 0.3 1100 0.4 0.4 0.6 11200.6 0.8 1.2 1140 1.0 1.4 2.3 1160 1.5 2.5 4.3 1180 2.3 4.1 7.5 1200 3.46.7 12.6

TABLE 28 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 1.5 89.6 625 415 210 30° 0.5 or less 0.5 or less 2.4 91.4 624 414210 40° 0.5 or less 0.5 or less 4.3 89.2 623 414 209

TABLE 29 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 0.49−2.08 −2.40 2.89 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range2.21 0.46 −0.95 3.16 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB)Range 1.72 2.54 1.45 1.09

TABLE 30 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.512.58 2.64 1.12 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.67 1.66 1.85 1.01 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.74 2.55 1.53 1.02

TABLE 31 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.020.05 0.11 0.10 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range0.06 0.02 0.08 0.07 ISE_(30/40) ^(CR) ISE_(30/40) ^(CG) ISE_(30/40)^(CB) Range 0.02 0.05 0.02 0.03

TABLE 32 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 1.1 1.0 0.8390 16.4 15.3 14.2 400 44.9 43.4 41.6 410 63.7 62.5 60.9 420 71.9 71.269.9 430 76.2 76.0 74.9 440 79.0 79.0 78.1 450 81.5 81.7 80.8 460 83.283.5 82.5 470 85.9 86.1 85.1 480 88.0 88.3 87.2 490 89.9 90.1 88.9 50090.8 90.9 89.7 510 91.5 91.5 90.2 520 92.5 92.5 91.2 530 92.2 92.1 90.7540 92.3 92.1 90.7 550 91.9 91.7 90.2 560 90.3 90.0 88.5 570 87.8 87.385.8 580 83.6 82.9 81.4 590 77.1 76.1 74.5 600 67.8 66.5 64.8 610 56.354.7 52.9 620 43.0 41.1 39.3 630 29.8 27.9 26.3 640 18.1 16.4 15.2 6509.4 8.2 7.4 660 4.2 3.5 3.0 670 1.6 1.3 1.0 680 0.5 0.4 0.3 690 0.1 0.10.1 700 0.0 0.0 0.0 710 0.0 0.0 0.0 715 0.0 0.0 0.0 730 0.0 0.0 0.0 7400.0 0.0 0.0 750 0.0 0.0 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.00.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 8600.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.00.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.0 0.0 0.0 1020 0.0 0.0 0.01040 0.0 0.0 0.0 1060 0.0 0.0 0.0 1080 0.0 0.0 0.0 1100 0.0 0.0 0.0 11200.0 0.0 0.0 1140 0.1 0.0 0.0 1160 0.2 0.1 0.1 1180 0.4 0.3 0.2 1200 0.70.5 0.4

TABLE 33 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 0.5 or less 87.8 615 402 213 30° 0.5 or less 0.5 or less 0.5 orless 87.5 614 403 211 40° 0.5 or less 0.5 or less 0.5 or less 86.1 612404 208

TABLE 34 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.21 0.460.18 1.03 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 2.592.23 1.40 1.19 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range1.38 1.77 1.23 0.54

TABLE 35 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 1.220.57 0.42 0.80 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range2.59 2.23 1.40 1.19 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 1.38 1.77 1.23 0.54

TABLE 36 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.020.002 0.002 0.02 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.07 0.03 0.01 0.06 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40)^(CB) Range 0.02 0.02 0.01 0.01

TABLE 37 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 2.4 0.3 0.3 380 0.3 1.6 11.8390 0.9 8.0 67.3 400 2.7 68.8 79.4 410 43.3 81.2 64.9 420 81.8 79.2 63.5430 81.4 81.1 81.1 440 82.4 86.1 83.2 450 88.4 89.4 84.5 460 91.5 91.591.1 470 93.2 95.0 91.4 480 95.2 96.1 93.1 490 93.8 96.2 93.0 500 95.396.8 89.8 510 95.7 96.5 90.9 520 93.5 95.4 94.1 530 92.9 95.7 92.7 54092.5 95.7 91.7 550 91.7 93.7 92.5 560 91.5 92.2 91.7 570 90.6 90.9 88.8580 88.4 88.4 86.2 590 85.7 84.9 84.0 600 81.7 80.8 79.8 610 75.8 75.173.3 620 68.0 67.1 65.3 630 59.3 57.9 56.1 640 51.1 49.4 44.9 650 43.441.5 29.2 660 34.4 32.0 16.7 670 23.0 17.9 6.3 680 11.7 5.6 1.2 690 4.81.0 0.2 700 1.9 0.1 0.0 710 1.0 0.1 0.0 715 0.9 0.1 0.0 730 0.8 0.1 0.0740 0.5 0.1 0.0 750 0.2 0.1 0.0 760 0.1 0.0 0.0 770 0.1 0.0 0.0 780 0.10.0 0.0 790 0.1 0.0 0.1 800 0.1 0.1 0.1 820 0.1 0.1 0.2 840 0.1 0.1 0.3860 0.1 0.2 0.6 880 0.1 0.3 0.9 900 0.2 0.5 0.7 920 0.3 0.5 0.5 940 0.40.4 0.4 960 0.4 0.3 0.4 980 0.4 0.3 0.4 1000 0.3 0.3 0.5 1020 0.2 0.30.6 1040 0.2 0.4 0.9 1060 0.2 0.5 1.5 1080 0.3 0.7 2.7 1100 0.4 1.2 5.41120 0.5 2.1 11.4 1140 0.7 4.1 21.5 1160 1.2 8.8 30.3 1180 2.1 18.9 36.31200 4.1 32.6 45.5

TABLE 38 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 1.3 91.1 641 411 230 30° 0.5 or less 0.5 or less 10.0 92.2 639 398241 40° 0.5 or less 0.5 or less 24.9 89.7 636 387 249

TABLE 39 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.30−1.59 −5.38 6.68 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range6.92 2.73 −0.57 7.49 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB)Range 5.62 4.32 4.82 1.30

TABLE 40 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 3.372.95 6.31 3.36 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range8.57 4.28 7.99 4.3 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40) ^(CB)Range 5.74 4.40 5.38 1.33

TABLE 41 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.120.07 1.48 1.41 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range0.81 0.11 1.47 1.36 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.45 0.12 0.3 0.33

TABLE 42 Transmittance [%] Incident Incident Incident Wavelength angleangle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0390 0.0 0.0 0.2 400 0.0 9.6 10.1 410 16.1 47.0 36.7 420 67.6 69.3 55.2430 79.9 78.7 78.6 440 84.8 84.9 82.0 450 86.6 88.2 83.3 460 90.9 90.489.9 470 91.7 92.7 89.2 480 91.9 93.7 90.7 490 95.0 94.3 91.2 500 93.394.0 87.1 510 94.2 94.8 89.2 520 93.7 92.7 91.4 530 94.6 93.8 90.9 54092.4 92.8 88.8 550 91.2 91.0 89.7 560 88.9 88.1 87.5 570 88.0 87.2 85.0580 83.0 82.5 80.3 590 78.6 78.0 77.0 600 73.0 72.1 70.9 610 66.6 65.463.4 620 59.9 58.2 56.2 630 50.4 48.8 47.0 640 42.7 40.8 36.8 650 35.834.6 24.1 660 28.6 26.9 13.9 670 20.4 15.8 5.5 680 11.2 5.5 1.1 690 4.50.9 0.2 700 1.5 0.1 0.0 710 0.8 0.0 0.0 715 0.5 0.0 0.0 730 0.2 0.1 0.0740 0.1 0.1 0.0 750 0.0 0.1 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.00.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0860 0.0 0.0 0.1 880 0.0 0.0 0.1 900 0.0 0.1 0.1 920 0.0 0.1 0.1 940 0.00.1 0.1 960 0.0 0.1 0.1 980 0.0 0.1 0.1 1000 0.0 0.1 0.1 1020 0.0 0.10.1 1040 0.0 0.1 0.2 1060 0.0 0.1 0.4 1080 0.0 0.2 0.7 1100 0.0 0.3 1.41120 0.0 0.6 3.2 1140 0.0 1.3 6.7 1160 0.0 3.0 10.5 1180 0.0 7.1 13.71200 0.4 13.4 18.7

TABLE 43 Average Average Average Average Full width transmittancetransmittance transmittance transmittance at half in wavelength inwavelength in wavelength in wavelength maximum range of range of rangeof range of IR cut-off UV cut-off in Incident 700 to 800 nm 700 to 1000nm 1100 to 1200 nm 500 to 600 nm wavelength wavelength transmissionangle θ [%] [%] [%] [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 orless 0.5 or less 88.8 630 414 216 30° 0.5 or less 0.5 or less 3.7 88.4629 411 218 40° 0.5 or less 0.5 or less 8.8 85.9 627 417 210

TABLE 44 IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB) Range 1.88 0.49−2.01 3.89 IE_(0/40) ^(CR) IE_(0/40) ^(CG) IE_(0/40) ^(CB) Range 6.924.66 2.40 4.51 IE_(30/40) ^(CR) IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range5.03 4.17 4.41 0.86

TABLE 45 IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30) ^(CB) Range 2.591.50 2.93 1.43 IAE_(0/40) ^(CR) IAE_(0/40) ^(CG) IAE_(0/40) ^(CB) Range7.41 5.05 5.30 2.37 IAE_(30/40) ^(CR) IAE_(30/40) ^(CG) IAE_(30/40)^(CB) Range 5.04 4.18 4.51 0.86

TABLE 46 ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30) ^(CB) Range 0.060.01 0.29 0.28 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range0.57 0.13 0.29 0.44 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB)Range 0.33 0.11 0.20 0.21

1. An optical filter comprising: a light-absorbing layer that includes alight absorber absorbing light in at least a portion of thenear-infrared region, wherein when light with a wavelength of 300 nm to1200 nm is incident on the optical filter at incident angles of 0°, 30°,and 40°, the optical filter satisfies the following requirements: (i)the spectral transmittance at a wavelength of 700 nm is 3% or less; (ii)the spectral transmittance at a wavelength of 715 nm is 1% or less;(iii) the spectral transmittance at a wavelength of 1100 nm is 7.5% orless; (iv) the average transmittance in the wavelength range of 700 nmto 800 nm is 1% or less; (v) the average transmittance in the wavelengthrange of 500 nm to 600 nm is 85% or more; (v1) the spectraltransmittance at a wavelength of 400 nm is 45% or less; and (vii) thespectral transmittance at a wavelength of 450 nm is 80% or more, and inthe case where the spectral transmittance of the optical filter at awavelength λ and an incident angle θ° is expressed by T_(θ)(λ), wherefunctions of the wavelength λ are expressed by R(λ), G(λ), and B(λ), thefunctions being defined by Table (I) in a domain ranging betweenwavelengths of 400 nm and 700 nm, where a normalization coefficient iscalculated so that the largest value of three functions being productsof T₀(λ) and R(λ), G(λ), and B(λ) is 1, where functions defined bymultiplying functions being products of T_(θ)(λ) and R(λ), G(λ), andB(λ) by the normalization coefficient are expressed by CR_(θ)(λ),CG_(θ)(λ), and CB_(θ)(λ), respectively, and where the wavelength λ beinga variable of CR_(θ)(λ), CG_(θ)(λ), and CB_(θ)(λ) is expressed byλ(n)=(Δλ×n+400) nm (Δλ=5) as a function of an integer n of 0 or more,IE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB) defined by thefollowing equations (1) to (3) for two incident angles θ1° and θ2°(θ1<θ2) selected from 0°, 30°, and 40° satisfy requirements shown inTable (II), and ranges satisfy requirements shown in Table (II), eachrange being a difference obtained by subtracting the smallest value ofIE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB) defined for thesame two incident angles θ1° and θ2° from the largest value ofIE_(θ1/θ2) ^(CR), IE_(θ1/θ2) ^(CG), and IE_(θ1/θ2) ^(CB) defined for thesame two incident angles θ1° and θ2°. TABLE I Wavelength λ [nm] R(λ)G(λ) B(λ) 400 0.100 0.066 0.429 405 0.089 0.067 0.492 410 0.079 0.0680.556 415 0.069 0.068 0.604 420 0.059 0.068 0.653 425 0.052 0.072 0.691430 0.045 0.076 0.728 435 0.040 0.082 0.769 440 0.035 0.089 0.811 4450.031 0.100 0.836 450 0.027 0.112 0.862 455 0.026 0.133 0.868 460 0.0250.153 0.875 465 0.026 0.213 0.863 470 0.027 0.272 0.850 475 0.030 0.3580.818 480 0.034 0.444 0.785 485 0.036 0.523 0.732 490 0.038 0.602 0.680495 0.042 0.669 0.615 500 0.046 0.737 0.549 505 0.056 0.797 0.478 5100.065 0.857 0.406 515 0.078 0.903 0.345 520 0.091 0.948 0.284 525 0.0960.974 0.245 530 0.101 1.000 0.206 535 0.096 0.998 0.183 540 0.091 0.9950.159 545 0.088 0.970 0.143 550 0.085 0.944 0.126 555 0.090 0.907 0.110560 0.096 0.870 0.093 565 0.141 0.825 0.085 570 0.186 0.780 0.076 5750.331 0.728 0.073 580 0.476 0.675 0.071 585 0.651 0.616 0.070 590 0.8260.556 0.070 595 0.897 0.485 0.066 600 0.968 0.414 0.062 605 0.968 0.3540.058 610 0.968 0.294 0.053 615 0.957 0.255 0.054 620 0.947 0.216 0.055625 0.932 0.200 0.055 630 0.918 0.184 0.055 635 0.899 0.173 0.058 6400.881 0.161 0.061 645 0.867 0.157 0.067 650 0.853 0.152 0.073 655 0.8370.155 0.078 660 0.822 0.157 0.084 665 0.795 0.168 0.087 670 0.767 0.1780.091 675 0.749 0.196 0.098 680 0.732 0.215 0.105 685 0.718 0.237 0.108690 0.705 0.259 0.111 695 0.704 0.277 0.115 700 0.702 0.296 0.119

$\begin{matrix}{{IE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (1) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (2) \\{{IE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\} \times \Delta \; \lambda}}} & (3)\end{matrix}$ TABLE II IE_(0/30) ^(CR) IE_(0/30) ^(CG) IE_(0/30) ^(CB)Range −5 to 5 −5 to 5 −5 to 5 0 to 4 IE_(0/40) ^(CR) IE_(0/40) ^(CG)IE_(0/40) ^(CB) Range −5 to 5 −5 to 5 −5 to 5 0 to 4 IE_(30/40) ^(CR)IE_(30/40) ^(CG) IE_(30/40) ^(CB) Range −3 to 3 −3 to 3 −3 to 3 0 to 1.3


2. The optical filter according to claim 1, wherein IAE_(θ1/θ2) ^(CR),IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB) defined by the followingequations (4) to (6) for two incident angles θ1° and θ2° (θ1<θ2)selected from 0°, 30°, and 40° satisfy requirements shown in Table(III), and ranges satisfy requirements shown in Table (III), each rangebeing a difference obtained by subtracting the smallest value ofIAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB) defined forthe same two incident angles θ1° and θ2° from the largest value ofIAE_(θ1/θ2) ^(CR), IAE_(θ1/θ2) ^(CG), and IAE_(θ1/θ2) ^(CB) defined forthe same two incident angles θ1° and θ2°. $\begin{matrix}{{IAE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (4) \\{{IAE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (5) \\{{IAE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{{{{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}}} \times \Delta \; \lambda}}} & (6)\end{matrix}$ TABLE III IAE_(0/30) ^(CR) IAE_(0/30) ^(CG) IAE_(0/30)^(CB) Range 0 to 6 0 to 6 0 to 6 0 to 4 IAE_(0/40) ^(CR) IAE_(0/40)^(CG) IAE_(0/40) ^(CB) Range 0 to 6 0 to 6 0 to 6 0 to 4 IAE_(30/40)^(CR) IAE_(30/40) ^(CG) IAE_(30/40) ^(CB) Range 0 to 4 0 to 4 0 to 4 0to 1.3


3. The optical filter according to claim 1, wherein ISE_(θ1/θ2) ^(CR),ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) defined by the followingequations (7) to (9) for two incident angles θ1° and θ2° (θ1<θ2)selected from 0°, 30°, and 40° satisfy requirements shown in Table (IV),and ranges satisfy requirements shown in Table (IV), each range being adifference obtained by subtracting the smallest value of ISE_(θ1/θ2)^(CR), ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) defined for the same twoincident angles θ1° and θ2° from the largest value of ISE_(θ1/θ2) ^(CR),ISE_(θ1/θ2) ^(CG), and ISE_(θ1/θ2) ^(CB) defined for the same twoincident angles θ1° and θ2°. $\begin{matrix}{{ISE}_{\theta \; {1/\theta}\; 2}^{CR} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CR}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CR}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (7) \\{{ISE}_{\theta \; {1/\theta}\; 2}^{CG} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CG}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CG}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (8) \\{{ISE}_{\theta \; {1/\theta}\; 2}^{CB} = {\sum\limits_{n = 0}^{300/{\Delta\lambda}}{\left\{ {{{CB}_{\theta \; 1}\left( {\lambda (n)} \right)} - {{CB}_{\theta \; 2}\left( {\lambda (n)} \right)}} \right\}^{2} \times \Delta \; \lambda}}} & (9)\end{matrix}$ TABLE IV ISE_(0/30) ^(CR) ISE_(0/30) ^(CG) ISE_(0/30)^(CB) Range 0 to 0.5 0 to 0.5 0 to 0.5 0 to 0.4 ISE_(0/40) ^(CR)ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range 0 to 0.5 0 to 0.5 0 to 0.5 0 to0.4 ISE_(0/40) ^(CR) ISE_(0/40) ^(CG) ISE_(0/40) ^(CB) Range 0 to 0.1 0to 0.1 0 to 0.1 0 to 0.08


4. The optical filter according to claim 1, wherein the light absorberis formed by a phosphonic acid and copper ion.
 5. The optical filteraccording to claim 4, wherein the phosphonic acid comprises a firstphosphonic acid having an aryl group.
 6. The optical filter according toclaim 5, wherein the phosphonic acid further comprises a secondphosphonic acid having an alkyl group.
 7. An imaging apparatuscomprising: a lens system; an imaging device that receives light havingbeen transmitted through the lens system; a color filter that isdisposed ahead of the imaging device and is a filter of three colors, R(red), G (green), and B (blue); and the optical filter according toclaim 1 that is disposed ahead of the color filter.